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Re: 奇数の完全数はない

 投稿者:うんざりはちべえ  投稿日:2017年10月14日(土)20時26分59秒
返信・引用
  したがって、奇数の完全数があるならば、m+1は素数ではないだろう。m+1は合成数であるはずだろう。  
 

Re: 奇数の完全数はない

 投稿者:うんざりはちべえ  投稿日:2017年10月14日(土)19時49分57秒
返信・引用 編集済
  1+x+x^2+x^3+・・・が最初の1+x+x^2と1+x+x^2+x^3+x^4を除いて因数分解できなくなっている。
つまり、m+1が素数なら、因数分解できなくなっている。
という事は、a=x^m y^n z^l・・・のとき、σ(x^m)が独自の素数をもつという事にならないだろうか?
つまり、σ(a)の素因数分解はaが奇数なら、aの素因数分解より1つ以上合成数が多いのであるが、それが、偶然的に素因数分解した時に数が一致することはないと言える方向を指し示しているのではなかろうか?
 

Re: 奇数の完全数はない

 投稿者:うんざりはちべえ  投稿日:2017年10月14日(土)19時39分27秒
返信・引用
  (%i1) x:210*n+19;
(%o1)                             210 n + 19
(%i2) factor(1+x+x^2);
                                    2
(%o2)                     3 (14700 n  + 2730 n + 127)
(%i3) factor(1+x+x^2+x^3+x^4);
                    4              3             2
(%o3)   1944810000 n  + 713097000 n  + 98078400 n  + 5997180 n + 137561
(%i4) factor(1+x+x^2+x^3+x^4+x^5+x^6);
                      6                   5                   4
(%o4) 85766121000000 n  + 46967161500000 n  + 10717847910000 n
                                   3                2
                  + 1304569287000 n  + 89330238900 n  + 3262718970 n + 49659541
(%i5) factor(1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^10);
                                10                             9
(%o5) 166798809782010000000000 n   + 151707488896971000000000 n
                            8                            7
+ 62093788212953700000000 n  + 15061224695518890000000 n
                           6                          5
+ 2397489679338768000000 n  + 261704778800459400000 n
                         4                        3                      2
+ 19838990337459300000 n  + 1031303351642130000 n  + 35183466327082500 n
+ 711317224168950 n + 6471681049901
(%i6) factor(1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^10+x^11+x^12);
                                    12                                 11
(%o6) 7355827511386641000000000000 n   + 8021354762416860900000000000 n
                                 10                                 9
+ 4009176191920392360000000000 n   + 1214474842503560106000000000 n
                                8                               7
+ 248333725473956696700000000 n  + 36110250501305947470000000 n
                              6                             5
+ 3828797382950916390000000 n  + 298271045847308990400000 n
                            4                          3
+ 16943267122951342950000 n  + 684433660818777975000 n
                         2
+ 18662943927245637600 n  + 308429532703201140 n + 2336276859014281
(%i7) factor(1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^10+x^11+x^12+x^13+x^14+x^15+x^16);
                                              16
(%o7) 14305686902419853283210000000000000000 n
                                           15
+ 20777307167800263101805000000000000000 n
                                           14
+ 14145437257753290754368600000000000000 n
                                          13
+ 5992311013941250825447320000000000000 n
                                          12
+ 1767886078787354392067124000000000000 n
                                         11
+ 385165618075291952273886000000000000 n
                                        10
+ 64102713691763641807805760000000000 n
                                       9                                      8
+ 8313259976827627473807624000000000 n  + 849028832772070681348291800000000 n
                                     7                                    6
+ 68513173853904386374724460000000 n  + 4353935202275346014252940000000 n
                                   5                                 4
+ 215603633673858231058622400000 n  + 8155792142431909886567160000 n
                                3                              2
+ 227829480105895910555292000 n  + 4432371341323193830094400 n
+ 53655444431236196839920 n + 304465936543600121441
(%i8) factor(1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^10+x^11+x^12+x^13+x^14+x^15+x^16+x^17+x^18);
                                                  18
(%o8) 630880792396715529789561000000000000000000 n
                                                17
+ 1030438627581302031989616300000000000000000 n
                                               16
+ 794781047237739788855297970000000000000000 n
                                               15
+ 384642112919256316601839845000000000000000 n
                                               14
+ 130888920815822448239556846600000000000000 n
                                              13
+ 33256758941876254691960504640000000000000 n
                                             12
+ 6538758180489841318406076060000000000000 n
                                             11
+ 1017199208363552627992079029200000000000 n
                                            10
+ 126923065783059458981062387260000000000 n
                                           9
+ 12797767904113080994329269514000000000 n
                                          8
+ 1045243078405217278465589184600000000 n
                                        7
+ 68985778920433892664699239100000000 n
                                       6                                      5
+ 3651958038220035820990729848000000 n  + 152963413125539471962457000400000 n
                                    4                                   3
+ 4957787790815321683189137960000 n  + 119982970721405026755254196000 n
                                 2
+ 2041683448580510588802188100 n  + 21799253613294196028310510 n
+ 109912203092239643840221
(%i9) factor(1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^10+x^11+x^12+x^13+x^14+x^15+x^16+x^17+x^18+x^19+x^20+x^21+x^22);
                                                            22
(%o9) 1226943273861056329490036128410000000000000000000000 n
                                                         21
+ 2448043960703726676458691132399000000000000000000000 n
                                                         20
+ 2331220042178951721185932363619100000000000000000000 n
                                                         19
+ 1409514314298104438323863336788310000000000000000000 n
                                                        18
+ 607216161776107850587864274323257000000000000000000 n
                                                        17
+ 198257123723298777402194194168648500000000000000000 n
                                                       16
+ 50946250006260853551635355911494170000000000000000 n
                                                       15
+ 10561429478737514101870786261597137000000000000000 n
                                                      14
+ 1796037161337414581795371558779364800000000000000 n
                                                     13
+ 253393230292942469111543413669096260000000000000 n
                                                    12
+ 29876888135088621337393907197957998000000000000 n
                                                   11
+ 2956131685822478110145754117171283800000000000 n
                                                  10
+ 245775133701202469399531170664571540000000000 n
                                                 9
+ 17147475929064799731415992225378282000000000 n
                                               8
+ 999823162717344918761516658403643400000000 n
                                              7
+ 48365241658001289058573685172339540000000 n
                                             6
+ 1919224591046115195888102506902425000000 n
                                           5
+ 61439187857209178257450497834888300000 n
                                          4
+ 1547972633312803755113151158535150000 n
                                        3
+ 29559220367457410242894379644875000 n
                                      2
+ 402170815937364614635566873986100 n  + 3474166282986237162969517914090 n
+ 14323868219183762624901448181
(%i10) factor(1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^10+x^11+x^12+x^13+x^14+x^15+x^16+x^17+x^18+x^19+x^20+x^21+x^22+x^23+x^24+x^25+x^26+x^27+x^28);
                                                                           28
(%o10) 105230165286103494342858306883583597610000000000000000000000000000 n
                                                                       27
+ 267084181416634107070207036042619321553000000000000000000000000000 n
                                                                       26
+ 326838689332611515354421496835787132241200000000000000000000000000 n
                                                                       25
+ 256766716522839178455774602047007320422900000000000000000000000000 n
                                                                       24
+ 145470045599770916039015086072956960973731000000000000000000000000 n
                                                                      23
+ 63295277156515889059189308646260693353024700000000000000000000000 n
                                                                      22
+ 21994092928500003217285678391366448246074940000000000000000000000 n
                                                                     21
+ 6266002135644603801297410941210331547994968000000000000000000000 n
                                                                     20
+ 1491012806346441402872762102533683769487240100000000000000000000 n
                                                                    19
+ 300353073091614847875775699730093329264499370000000000000000000 n
                                                                   18
+ 51730967494914926998712635306109561932883664000000000000000000 n
                                                                  17
+ 7673562742321688791306378073333903851831219800000000000000000 n
                                                                 16
+ 985446534505911141387078130696949280382248510000000000000000 n
                                                                 15
+ 109946083226537201927751216433087910421927327000000000000000 n
                                                                14
+ 10678611379413884047167370933953719540102219400000000000000 n
                                                              13
+ 903493624788041694086078546853658650061691880000000000000 n
                                                             12
+ 66546273721815368751643550376001284289575411000000000000 n
                                                            11
+ 4258269073488516677436096612181819989097562700000000000 n
                                                           10
+ 235902245947092185864995493879470622000769240000000000 n
                                                          9
+ 11255350907222240111356094177078878537419198000000000 n
                                                        8
+ 459149267291634131159718851412781817978192100000000 n
                                                       7
+ 15856550527224618703424122023685522633262370000000 n
                                                     6
+ 457372445160710699329559642312641593753834000000 n
                                                    5
+ 10816360024886324370068060368563699829060800000 n
                                                  4
+ 204281684625727148139749919324316587110910000 n
                                                3
+ 2963062180233701386846282761556576089411000 n
                                              2
+ 30994301317945613544385045093605221949600 n
+ 208134031398385234476053918597591855460 n
+ 673878999699401213583361167853606121
(%i11) factor(1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^10+x^11+x^12+x^13+x^14+x^15+x^16+x^17+x^18+x^19+x^20+x^21+x^22+x^23+x^24+x^25+x^26+x^27+x^28+x^29+x^30);
(%o11) 4640650289117164100520051333566036654601000000000000000000000000000000
  30
n   + 12618149119456670006652139578410509189415100000000000000000000000000000
  29
n   + 16582906056941191363008012006863288396567070000000000000000000000000000
  28
n   + 14028002329022852575080288235033989721015299000000000000000000000000000
  27
n   + 8582216175651226798440592780510239550655352300000000000000000000000000
  26
n   + 4044865471153267560924123529501262768111429550000000000000000000000000
  25
n   + 1527550496317364237264713546128758163520558851000000000000000000000000
  24
n   + 474693150804859289261522876491779988570698026700000000000000000000000
  23
n   + 123696229349510505362482277931877187804220186390000000000000000000000
  22                                                                         21
n   + 27405879488952519158514715286092841989898781663000000000000000000000 n
                                                                        20
+ 5216408812887900113128984419860236289555768231100000000000000000000 n
                                                                       19
+ 859644696931880553229493130379343155954652704470000000000000000000 n
                                                                       18
+ 123368102121102046536330303934445567860241295999000000000000000000 n
                                                                      17
+ 15482641765625591166944314612134371397568408578300000000000000000 n
                                                                     16
+ 1704042704936553079904270970504999247103479657110000000000000000 n
                                                                    15
+ 164749923705655363301509873101541764060052087767000000000000000 n
                                                                   14
+ 13999548504909042621781808282631145418639478030900000000000000 n
                                                                  13
+ 1044990128989413279678121748011879282822285063530000000000000 n
                                                                12
+ 68407481066280476601929673931032041571769197201000000000000 n
                                                               11
+ 3916096033195650952667898671364991123130545301700000000000 n
                                                              10
+ 195226893714094820370028606170882023443721167290000000000 n
                                                            9
+ 8426466708745074731675110213444005607601173953000000000 n
                                                           8
+ 312458283531119720442416579335012201188105140100000000 n
                                                         7
+ 9851048329808045637305995458459012751224892170000000 n
                                                        6
+ 260434827993603998164077124058204301472630389000000 n
                                                      5
+ 5665544854445571970909695219044187008979035700000 n
                                                    4
+ 98757773036273839102790437801927755428515650000 n
                                                   3
+ 1326178682366240985576094714579047440260965000 n
                                                 2
+ 12879570410224224254160937776702612160312500 n
+ 80513939752418291330250686733202436666850 n
+ 243270318891483838103593381595151809701
(%i12) factor(1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^10+x^11+x^12+x^13+x^14+x^15+x^16+x^17+x^18+x^19+x^20+x^21+x^22+x^23+x^24+x^25+x^26+x^27+x^28+x^29+x^30+x^31+x^32+x^33+x^34+x^35+x^36);
(%o12) 39801057421510767942205888560083606120894457272100000000000000000000000\
               36
0000000000000 n   + 1298272587320708382876715888745584294895843011018500000000\
                             35
000000000000000000000000000 n   + 20586081618178957198515633462586916602611206\
                                           34
63477760000000000000000000000000000000000 n   + 211398591166351533754488573051\
                                                         33
1998268616837741290422000000000000000000000000000000000 n   + 1580257128670853\
                                                                       32
912800989254797122097078174220011716900000000000000000000000000000000 n   + 91\
639021042742235757868090076204023286673622466632661000000000000000000000000000\
      31
0000 n   + 4290072037454768434144199583692892240416887462349679660000000000000\
                   30
00000000000000000 n   + 166595203858517153612676473800211019768145559605890282\
                                29
000000000000000000000000000000 n   + 54720013740395512969450074033548144181196\
                                            28
225336490124600000000000000000000000000000 n   + 15425470280477910264562614802\
                                                        27
093829156518990445727130500000000000000000000000000000 n   + 37738086501382189\
                                                                   26
54539506564888963446551063101066618865600000000000000000000000000 n   + 808237\
                                                                             25
960784531451712553173263119666915376586088231624400000000000000000000000000 n
display: failed to break up a long expression.
display: change 'linel' slightly and try again.
-- an error. To debug this try: debugmode(true);
(%i13)
 

Re: 奇数の完全数はない

 投稿者:うんざりはちべえ  投稿日:2017年10月12日(木)13時31分23秒
返信・引用
  (%i14) x:210*n+17;
(%o14)                            210 n + 17
(%i15) factor(1+x+x^2);
                                   2
(%o15)                      44100 n  + 7350 n + 307
(%i16) factor(1+x+x^2+x^3+x^4);
                    4              3             2
(%o16)  1944810000 n  + 639009000 n  + 78762600 n  + 4316340 n + 88741
(%i17) factor(1+x+x^2+x^3+x^4+x^5+x^6);
                       6                   5                  4
(%o17) 85766121000000 n  + 42066240300000 n  + 8598005010000 n
                                   3                2
                   + 937389159000 n  + 57494537100 n  + 1881033210 n + 25646167
(%i18) factor(1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^10);
                                 10                             9
(%o18) 166798809782010000000000 n   + 135821887965351000000000 n
                            8                            7
+ 49771100633139900000000 n  + 10808350345426410000000 n
                           6                          5
+ 1540386463721994000000 n  + 150543601793991000000 n
                         4                       3                      2
+ 10217670623789580000 n  + 475559138331522000 n  + 14526021813225300 n
+ 262945454437470 n + 2141993519227
(%i19) factor(1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^10+x^11+x^12);
                                     12                                 11
(%o19) 7355827511386641000000000000 n   + 7180688761115530500000000000 n
                                 10                                9
+ 3212878674021076620000000000 n   + 871266434375910006000000000 n
                                8                               7
+ 159486512599461933900000000 n  + 20760945439918272750000000 n
                              6                             5
+ 1970652279333872484000000 n  + 137433427172741120400000 n
                           4                          3
+ 6988996619925491430000 n  + 252748281264930927000 n
                        2
+ 6169912762903558200 n  + 91285070059709820 n + 619036127056621
(%i20) factor(1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^10+x^11+x^12+x^13+x^14+x^15+x^16);
                                               16
(%o20) 14305686902419853283210000000000000000 n
                                           15
+ 18597392973145809268173000000000000000 n
                                           14
+ 11332958676257142727941600000000000000 n
                                          13
+ 4297211466268578202553040000000000000 n
                                          12
+ 1134784657690708883385996000000000000 n
                                         11
+ 221296659677766814336902000000000000 n
                                        10
+ 32966535767929800243888240000000000 n
                                       9                                      8
+ 3826830398771534377509720000000000 n  + 349834527794597476964319000000000 n
                                     7                                    6
+ 25269004972850857615536300000000 n  + 1437379019088153713133912000000 n
                                  5                                 4
+ 63712138960673743462725600000 n  + 2157299948592466191211320000 n
                               3                             2
+ 53942876878375875440988000 n  + 939380786415629310967200 n
+ 10178932909929534402960 n + 51702516367896047761
(%i21) factor(1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^10+x^11+x^12+x^13+x^14+x^15+x^16+x^17+x^18);
                                                   18
(%o21) 630880792396715529789561000000000000000000 n
                                               17
+ 922287634599007941168548700000000000000000 n
                                               16
+ 636703206966000410075827470000000000000000 n
                                               15
+ 275798997180159436688594085000000000000000 n
                                              14
+ 84001318330756224371926251600000000000000 n
                                              13
+ 19103439261452797040171218200000000000000 n
                                             12
+ 3361835143537574112419504508000000000000 n
                                            11
+ 468099020615718049132905363600000000000 n
                                           10
+ 52278600559902216460029570060000000000 n
                                          9
+ 4718135633001122241470697570000000000 n
                                         8
+ 344911288780581372966822892200000000 n
                                        7
+ 20375333961609027449372321340000000 n
                                      6                                     5
+ 965444136428614710451980564000000 n  + 36194810662921296572924094000000 n
                                    4                                  3
+ 1050038518735755732522379320000 n  + 22745561174186113749921876000 n
                                2
+ 346438709222837962212915300 n  + 3310867577836413223469190 n
+ 14942027230321957802947
(%i22) factor(1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^10+x^11+x^12+x^13+x^14+x^15+x^16+x^17+x^18+x^19+x^20+x^21+x^22);
                                                             22
(%o22) 1226943273861056329490036128410000000000000000000000 n
                                                         21
+ 2190970131894743445517921657875000000000000000000000 n
                                                         20
+ 1867318632919104708988271084591700000000000000000000 n
                                                         19
+ 1010469595491333931421370213068310000000000000000000 n
                                                        18
+ 389597682073456033345117983274479000000000000000000 n
                                                        17
+ 113847059345613039179986448742102900000000000000000 n
                                                       16
+ 26183392171478366466723734072708190000000000000000 n
                                                      15
+ 4858002881204941933062450710936337000000000000000 n
                                                     14
+ 739388123180020677208022109362644200000000000000 n
                                                    13
+ 93363035794009687761687564297967980000000000000 n
                                                   12
+ 9852327662982760599420840126198786000000000000 n
                                                  11
+ 872472049026603470603698549887019800000000000 n
                                                 10
+ 64921819832809469656898984349259500000000000 n
                                                9
+ 4053952808695112197556849014969002000000000 n
                                               8
+ 211557377866276619932734968578291800000000 n
                                             7
+ 9159369889748693595537563889219540000000 n
                                            6
+ 325301492368694510156015705240973000000 n
                                          5
+ 9320399253401838061345520922611100000 n
                                         4
+ 210175410314731224361881561748650000 n
                                       3                                     2
+ 3592046621615957459156194569675000 n  + 43741200914411681822201045981100 n
+ 338191521985835362933508440650 n + 1247973056303720237659941607
(%i23) factor(1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^10+x^11+x^12+x^13+x^14+x^15+x^16+x^17+x^18+x^19+x^20+x^21+x^22+x^23+x^24+x^25+x^26+x^27+x^28);
                                                                           28
(%o23) 105230165286103494342858306883583597610000000000000000000000000000 n
                                                                       27
+ 239022804007006508578778154206997028857000000000000000000000000000 n
                                                                       26
+ 261767791206714864770980543803693601474200000000000000000000000000 n
                                                                       25
+ 184040525560687949942448053667369470318700000000000000000000000000 n
                                                                      24
+ 93312691260891706293037986994872503988231000000000000000000000000 n
                                                                      23
+ 36335510456527356827842398742479026358795900000000000000000000000 n
                                                                      22
+ 11299500731907685102196469934655153110595160000000000000000000000 n
                                                                     21
+ 2880961131514436068845718237785533558958204000000000000000000000 n
                                                                    20
+ 613510953610463024286035941760139171965936100000000000000000000 n
                                                                    19
+ 110603161849852531875941371250093204461591290000000000000000000 n
                                                                   18
+ 17048297291531393553348343211856417741820506000000000000000000 n
                                                                  17
+ 2263199500782543813083340262977714484327979400000000000000000 n
                                                                 16
+ 260108578208752459792911289230792717344605110000000000000000 n
                                                                15
+ 25971535682800212685809848954866101338852799000000000000000 n
                                                               14
+ 2257508279959696872192603187880563989924453600000000000000 n
                                                              13
+ 170937288991228893281195591500646213198460240000000000000 n
                                                             12
+ 11267642542091383889890183678538470787616411000000000000 n
                                                           11
+ 645268510400409023851652320060208066872593900000000000 n
                                                          10
+ 31991746956315270642300847317822497292954660000000000 n
                                                         9
+ 1366041485143045231749387663230986725856194000000000 n
                                                       8
+ 49872159794979151187021080853402619923318100000000 n
                                                      7
+ 1541391269527184912218206308598631704181890000000 n
                                                    6
+ 39790055378397779184436233538414931819676000000 n
                                                  5
+ 842144317700226953868967918611927417836400000 n
                                                 4
+ 14234300721218570881405567833044999098110000 n
                                               3
+ 184777577654149835334982364767614147771000 n
                                             2
+ 1729787030979011994321251164430243415000 n
+ 10395769729701449540356348353329443980 n
+ 30123035756671932193213239076441981
(%i24) factor(1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^10+x^11+x^12+x^13+x^14+x^15+x^16+x^17+x^18+x^19+x^20+x^21+x^22+x^23+x^24+x^25+x^26+x^27+x^28+x^29+x^30);
(%o24) 4640650289117164100520051333566036654601000000000000000000000000000000
  30
n   + 11292249036851765977932124911677355859529100000000000000000000000000000
  29
n   + 13280993930593835917517804053470202270760490000000000000000000000000000
  28
n   + 10054286796800307607906027136055188096920131000000000000000000000000000
  27
n   + 5504789928767376806030867706818162894782548900000000000000000000000000
  26
n   + 2321836338622662036573508499196584517820972830000000000000000000000000
  25
n   + 784710894711131943876347029381110654031648041000000000000000000000000
  24
n   + 218229783647543908389025422856356261777398253900000000000000000000000
  23                                                                         22
n   + 50891451244755813897107393060526186343621359810000000000000000000000 n
                                                                         21
+ 10090665413364874673027723667016523203131880599000000000000000000000 n
                                                                        20
+ 1718841151757905347315547713537213722968201658100000000000000000000 n
                                                                       19
+ 253496254420651713840029532421248967524862187190000000000000000000 n
                                                                      18
+ 32556990651845919039200108520965344980384984501000000000000000000 n
                                                                     17
+ 3656584627748137104346686280018014556854674967900000000000000000 n
                                                                    16
+ 360164259023745611520527484710975930827668265410000000000000000 n
                                                                   15
+ 31162717375754691327354958694602028177041154199000000000000000 n
                                                                  14
+ 2369815172411956723635555944835643517059056929100000000000000 n
                                                                 13
+ 158308185577655669083939304723106612787017574890000000000000 n
                                                               12
+ 9274401899696833809804528015043475785710763731000000000000 n
                                                              11
+ 475146102268617534999303566295139276608134064900000000000 n
                                                             10
+ 21198513321255036737663202455955002478895450110000000000 n
                                                           9
+ 818848565128640066079726450176249528179352649000000000 n
                                                          8
+ 27173329287360417028320723309071686018945337100000000 n
                                                        7
+ 766701636705696591673557815860073174827638090000000 n
                                                       6
+ 18139969094542317610796487972928361519464911000000 n
                                                     5
+ 353161306139414193499640205093040101231926100000 n
                                                   4
+ 5509308420948971237967550364542143489040230000 n
                                                 3
+ 66209852788319281975993351694254255168437000 n
                                               2
+ 575462673699872048286706617606383668314300 n
+ 3219455927186356513022527201118005054770 n
+ 8705557333678188403838626093091732527
(%i25) factor(1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^10+x^11+x^12+x^13+x^14+x^15+x^16+x^17+x^18+x^19+x^20+x^21+x^22+x^23+x^24+x^25+x^26+x^27+x^28+x^29+x^30+x^31+x^32+x^33+x^34+x^35+x^36);
(%o25) 39801057421510767942205888560083606120894457272100000000000000000000000\
               36
0000000000000 n   + 1161811819018385749932009985111011931052776300371300000000\
                             35
000000000000000000000000000 n   + 16485940940947133643834423672825922892696841\
                                           34
11579460000000000000000000000000000000000 n   + 151499963798726195393861496438\
                                                         33
4037867362290584101794000000000000000000000000000000000 n   + 1013465187678758\
                                                                       32
302165261758890263383754261248933302100000000000000000000000000000000 n   + 52\
593539844900244625971019585404366571638026774444693000000000000000000000000000\
      31
0000 n   + 2203371250175285805221465365658702969115425000004271680000000000000\
                   30
00000000000000000 n   + 765697043245856962078618303633200277459068587387703408\
                               29
00000000000000000000000000000 n   + 225067251163868984321297952667886458292937\
                                           28
50022754088520000000000000000000000000000 n   + 567775185561181092914690555053\
                                                      27
8695469107211491305284948000000000000000000000000000 n   + 1243054039965538303\
                                                                 26
213807648720204439831872459719532533600000000000000000000000000 n   + 23824389\
                                                                           25
0378818966859722661155633744350302085081999239600000000000000000000000000 n
display: failed to break up a long expression.
display: change 'linel' slightly and try again.
-- an error. To debug this try: debugmode(true);
(%i26)
 

Re: 奇数の完全数はない

 投稿者:うんざりはちべえ  投稿日:2017年10月12日(木)13時30分19秒
返信・引用
  (%i1) x:210*n+13;
(%o1)                             210 n + 13
(%i2) factor(1+x+x^2);
                                    2
(%o2)                     3 (14700 n  + 1890 n + 61)
(%i3) factor(1+x+x^2+x^3+x^4);
                    4              3             2
(%o3)   1944810000 n  + 490833000 n  + 46481400 n  + 1957620 n + 30941
(%i4) factor(1+x+x^2+x^3+x^4+x^5+x^6);
                      6                   5                  4
(%o4) 85766121000000 n  + 32264397900000 n  + 5058450810000 n
                                     3                2
                     + 423070263000 n  + 19908459900 n  + 499775850 n + 5229043
(%i5) factor(1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^10);
                                10                             9
(%o5) 166798809782010000000000 n   + 104050686102111000000000 n
                            8                           7
+ 29210594284500300000000 n  + 4859859199294890000000 n
                          6                         5                        4
+ 530650600061022000000 n  + 39734701369738200000 n  + 2066344238030940000 n
                      3                     2
+ 73690811657442000 n  + 1724761068074100 n  + 23924192439630 n + 149346699503
(%i6) factor(1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^10+x^11+x^12);
                                    12                                 11
(%o6) 7355827511386641000000000000 n   + 5499356758512869700000000000 n
                                 10                                9
+ 1884492952917148980000000000 n   + 391394201433533046000000000 n
                               8                              7
+ 54873113124921720300000000 n  + 5470968811419471150000000 n
                             6                            5
+ 397757201786247744000000 n  + 21247168865227880400000 n
                          4                         3                       2
+ 827625970978929990000 n  + 22925999488379967000 n  + 428696900672985000 n
+ 4858621501584060 n + 25239592216021
(%i7) factor(1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^10+x^11+x^12+x^13+x^14+x^15+x^16);
                                              16
(%o7) 14305686902419853283210000000000000000 n
                                           15
+ 14237564583836901600909000000000000000 n
                                          14
+ 6642250453831041175215600000000000000 n
                                          13
+ 1928198365681003889543280000000000000 n
                                         12
+ 389830935382258749310764000000000000 n
                                        11
+ 58202341934244801177855600000000000 n
                                       10
+ 6638143699001007828749520000000000 n
                                      9                                     8
+ 589963780984083465563352000000000 n  + 41292079270600703392776600000000 n
                                    7                                  6
+ 2283575657150638737876780000000 n  + 99455103677286919897776000000 n
                                 5                               4
+ 3375296175937037974524000000 n  + 87506371964197299125880000 n
                              3                            2
+ 1675360629679189314204000 n  + 22339149929825174863200 n
+ 185346251349564884880 n + 720867993281778161
(%i8) factor(1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^10+x^11+x^12+x^13+x^14+x^15+x^16+x^17+x^18);
                                                  18
(%o8) 630880792396715529789561000000000000000000 n
                                               17
+ 705985648634419759526413500000000000000000 n
                                               16
+ 373078008728207353772833590000000000000000 n
                                               15
+ 123706383819118192716089445000000000000000 n
                                              14
+ 28842047653673338040122437600000000000000 n
                                             13
+ 5021065710287418160513017720000000000000 n
                                            12
+ 676408352166522788312464524000000000000 n
                                           11
+ 72097863124830954975373798800000000000 n
                                          10
+ 6164029225137757064656018860000000000 n
                                         9
+ 425864318284133114545132722000000000 n
                                        8
+ 23832654556942359549678385800000000 n
                                       7                                     6
+ 1077799713495267904019541180000000 n  + 39096060645698817695076492000000 n
                                    5                                  4
+ 1122093248426728919678257200000 n  + 24921202411903007419294680000 n
                                3                              2
+ 413281474717144260276756000 n  + 4819097149012805240225700 n
+ 35259455721394974303990 n + 121826690864620509223
(%i9) factor(1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^10+x^11+x^12+x^13+x^14+x^15+x^16+x^17+x^18+x^19+x^20+x^21+x^22);
                                                            22
(%o9) 1226943273861056329490036128410000000000000000000000 n
                                                         21
+ 1676822474276776983636382708827000000000000000000000 n
                                                         20
+ 1093760111684800623157410211251300000000000000000000 n
                                                        19
+ 452983455663516616877831413213110000000000000000000 n
                                                        18
+ 133669812894537061948141578091563000000000000000000 n
                                                       17
+ 29895040884150266100360145489430100000000000000000 n
                                                      16
+ 5262184903577672421332704840633110000000000000000 n
                                                     15
+ 747245572078704701198241088768977000000000000000 n
                                                    14
+ 87045434735320308775025685062547000000000000000 n
                                                   13
+ 8412382794856314039112127522832300000000000000 n
                                                  12
+ 679447740251629848421532871936234000000000000 n
                                                 11
+ 46051579570652996894567522224795800000000000 n
                                                10
+ 2622781841022480401397240537171420000000000 n
                                               9
+ 125352025322255662262800281652314000000000 n
                                             8
+ 5006852137874099840172576919990200000000 n
                                            7
+ 165916235477509612897185794086740000000 n
                                          6
+ 4510231627611251352317718992949000000 n
                                        5
+ 98909874107276914356712572282300000 n
                                       4                                     3
+ 1707191549275946444585354790450000 n  + 22332659114405473684304943195000 n
                                   2
+ 208156626883744308803744027100 n  + 1231874036315601718457232570 n
+ 3479492117784426363920483
(%i10) factor(1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^10+x^11+x^12+x^13+x^14+x^15+x^16+x^17+x^18+x^19+x^20+x^21+x^22+x^23+x^24+x^25+x^26+x^27+x^28);
                                                                           28
(%o10) 105230165286103494342858306883583597610000000000000000000000000000 n
                                                                       27
+ 182900049187751311595920390535752443465000000000000000000000000000 n
                                                                       26
+ 153273343242348568154629489441272308591400000000000000000000000000 n
                                                                      25
+ 82459611962661876854654251031570313720300000000000000000000000000 n
                                                                      24
+ 31992443586831485787322115062338053226831000000000000000000000000 n
                                                                     23
+ 9532752708669176887971098785679078846178300000000000000000000000 n
                                                                     22
+ 2268444615669023423815107247133859580985040000000000000000000000 n
                                                                    21
+ 442577878575190846320999010855556511116172000000000000000000000 n
                                                                   20
+ 72120632868838444327498040264456096585816100000000000000000000 n
                                                                  19
+ 9949269486312867998224741382530125666704730000000000000000000 n
                                                                  18
+ 1173525844554136656348302227372990285598334000000000000000000 n
                                                                 17
+ 119213118745441642955163125641882102398088200000000000000000 n
                                                                16
+ 10484483212012212363716205081434105172494310000000000000000 n
                                                              15
+ 801092598564238506683793491302715630846463000000000000000 n
                                                             14
+ 53285467970719283310624414010693776821600400000000000000 n
                                                            13
+ 3087537270972160012197344933910869196022320000000000000 n
                                                           12
+ 155742111364809210210869183444079341364411000000000000 n
                                                         11
+ 6825158152594628264220791019950993157936300000000000 n
                                                        10
+ 258947140025485670679724293973209893227740000000000 n
                                                      9
+ 8461349731945891967740540330366520664642000000000 n
                                                     8
+ 236394965568942791162770314021248079458100000000 n
                                                   7
+ 5591121638886193924244876602237568254530000000 n
                                                  6
+ 110450659620144802635033496251634003104000000 n
                                                5
+ 1788915215834662509025292241218025745200000 n
                                              4
+ 23139320092731404590302309763619134110000 n
                                            3
+ 229867049228790875744497924095651531000 n
                                          2
+ 1646777298074668278997954506258299400 n
+ 7573828629634024817668137463009740 n + 16794843869550929233208663030981
(%i11) factor(1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^10+x^11+x^12+x^13+x^14+x^15+x^16+x^17+x^18+x^19+x^20+x^21+x^22+x^23+x^24+x^25+x^26+x^27+x^28+x^29+x^30);
(%o11) 4640650289117164100520051333566036654601000000000000000000000000000000
  30
n   + 8640448871641957920492095578211049199757100000000000000000000000000000
  29
n   + 7775772603486045507476828870548642778195730000000000000000000000000000
  28
n   + 4504251449969341923074240028842139802919859000000000000000000000000000
  27
n   + 1886999438503359278865449868597057080368031700000000000000000000000000
  26
n   + 609008810858100470346740773113148530753690990000000000000000000000000
  25
n   + 157493960306512159896625866413946109016908221000000000000000000000000
  24                                                                         23
n   + 33514427254483875110853657642860679777405636300000000000000000000000 n
                                                                        22
+ 5980362266584382374380071299699474679315260890000000000000000000000 n
                                                                       21
+ 907337101289462637778099227648097879638867567000000000000000000000 n
                                                                       20
+ 118263888094939382906614384980456438058097276100000000000000000000 n
                                                                      19
+ 13346176191126437289684405295911118912795692630000000000000000000 n
                                                                     18
+ 1311595205729499030697938386521955675466679089000000000000000000 n
                                                                    17
+ 112720479002249235310068340944558048867424856700000000000000000 n
                                                                  16
+ 8495732388499526529960087779146786676405804010000000000000000 n
                                                                 15
+ 562483697927355851043473312114016294603574743000000000000000 n
                                                                14
+ 32731424697747638716392360296844493047302859900000000000000 n
                                                               13
+ 1673135201375576436264833919415448896242446970000000000000 n
                                                             12
+ 75005349208943344925258252335200387624260991000000000000 n
                                                            11
+ 2940448635506457774341966156034607422025407300000000000 n
                                                           10
+ 100386054182322025579014926733610715088535590000000000 n
                                                         9
+ 2967253080980164534356076288546633266190497000000000 n
                                                       8
+ 75349147418718336329090186502505107635039100000000 n
                                                      7
+ 1626851319516066012232682423149785627326730000000 n
                                                    6
+ 29454082570351183887031088364152170907619000000 n
                                                  5
+ 438804496053361110708657358527825055696500000 n
                                                4
+ 5238242063305898428429858809339882027390000 n
                                              3
+ 48172941209720207298608145638454152997000 n
                                            2
+ 320399120307067910634306844145352041100 n
+ 1371676885935898267799234531397802530 n + 2838328613954107040412264052235803
(%i12) factor(1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^10+x^11+x^12+x^13+x^14+x^15+x^16+x^17+x^18+x^19+x^20+x^21+x^22+x^23+x^24+x^25+x^26+x^27+x^28+x^29+x^30+x^31+x^32+x^33+x^34+x^35+x^36);
(%o12) 39801057421510767942205888560083606120894457272100000000000000000000000\
               36
0000000000000 n   + 8888902824137404840425981778418672033666428790769000000000\
                            35
00000000000000000000000000 n   + 965026726950671286391906312964965911129877718\
                                         34
430060000000000000000000000000000000000 n   + 67850372370648971679891475834318\
                                                      33
9308017383299806658000000000000000000000000000000000 n   + 3472670060046560072\
                                                                   32
05016316265769062006752639708366900000000000000000000000000000000 n   + 137880\
532720824503675272233666145955431187080627691730000000000000000000000000000000
  31
n   + 44195187368585052658613407448379073990501375215300900000000000000000000\
              30
000000000000 n   + 11750650657788856421684900184568824124032743270451974400000\
                          29
000000000000000000000000 n   + 26426265546963209804907496719208992848450340292\
                                     28
66760520000000000000000000000000000 n   + 510057741624167192339694979596374303\
                                               27
194810034942816916000000000000000000000000000 n   + 85438438711419176821472937\
                                                        26
236890492906814455397521879200000000000000000000000000 n   + 12528709552791507\
                                                                 25
227693951015428823611298570750177646000000000000000000000000000 n   + 16193460\
                                                                         24
59323964825480245271733556525234964481206700756000000000000000000000000 n   + \
185474548929521000949416210804110122387324813123528046800000000000000000000000
  23
n   + 18904408820436733682067354246982063057130562627945215040000000000000000\
        22
000000 n   + 17201872380677782707806024897917292137920093568549804320000000000\
             21
00000000000 n
+ 140074301518136072933764530788167765153523746660183236600000000000000000000
  20
n
+ 10224103002411408979441779121886429000209659520025304780000000000000000000
  19
n   + 669567312268664608872999968688982150719238276070553684000000000000000000
  18
n   + 39355310747224475479733504227641024391921698936479905200000000000000000
  17
n   + 2075461815542978891849115302439721302138094941662301660000000000000000
  16                                                                         15
n   + 98109305347645520339396946974215971288691661277748758000000000000000 n
                                                                        14
+ 4150265162550983297118206244560672590993270498621706400000000000000 n
                                                                       13
+ 156738404908309466341524369219844554907564779856429920000000000000 n
                                                                     12
+ 5267556898859012471791222580580847644073044944619876000000000000 n
                                                                    11
+ 156875278790421918042299217765138901282623045008931600000000000 n
                                                                  10
+ 4117942073512863520083242889291292851636149644022160000000000 n
                                                                9
+ 94629209868262424592442592981453189980928107219320000000000 n
                                                               8
+ 1887212516827854392177512418947806810801298612218000000000 n
                                                             7
+ 32301768288154842101226267184926241567950634809000000000 n
                                                           6
+ 467647889516219176172041855619975928334840922688000000 n
                                                         5
+ 5615996642756926332109497378249342594662519467200000 n
                                                       4
+ 54446202043382272389225393518987183806971090330000 n
                                                     3
+ 409483870895967006988490930756330706668181609000 n
                                                   2
+ 2241840660856372234505177786117593080590038200 n
+ 7948675286164053636446051782762648748104980 n
+ 13700070098791209449625279837708244444861
(%i13) factor(1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^10+x^11+x^12+x^13+x^14+x^15+x^16+x^17+x^18+x^19+x^20+x^21+x^22+x^23+x^24+x^25+x^26+x^27+x^28+x^29+x^30+x^31+x^32+x^33+x^34+x^35+x^36+x^37+x^38+x^39+x^40);
(%o13) 77405494483928356601681434130536198019976749447352801000000000000000000\
                        40
0000000000000000000000 n   + 1920393458386984466165525103905207579447994593431\
                                               39
943301000000000000000000000000000000000000000 n   + 23226562979748915130129933\
                                                                      38
82228025852967683288178979920800000000000000000000000000000000000000 n   + 182\
477406072201763449936681911060710529399208722768591844000000000000000000000000\
               37
0000000000000 n   + 1046922024158839730931699098910131512121472366338265624102\
                                      36
000000000000000000000000000000000000 n   + 46753275299034243264399937693673991\
                                                            35
4732046685875030689107000000000000000000000000000000000000 n   + 1691592510444\
176894466644381161700297853030657850463032921200000000000000000000000000000000\
    34
00 n   + 509618596702230381179976124771798087301909192102061064205160000000000\
                         33
00000000000000000000000 n   + 130388588185317385897925586801588739804901350644\
                                              32
48586409229300000000000000000000000000000000 n   + 287553823769093650433199317\
                                                                  31
1232127362982773637663442292010490000000000000000000000000000000 n   + 5529102\
949591361726746511302837690154050248606777481093565640000000000000000000000000\
       30
00000 n   + 935317002754026149698287256246709185612959351327789153321888000000\
                         29
00000000000000000000000 n   + 140201583836660173421366577012444040910280883539\
                                           28
89455627077840000000000000000000000000000 n   + 187303848357205877371719420659\
                                                            27
4739280369643103173456215969832000000000000000000000000000 n   + 2240594684218\
                                                                            26
96830056126715877024661240079689110536767133777600000000000000000000000000 n
display: failed to break up a long expression.
display: change 'linel' slightly and try again.
-- an error. To debug this try: debugmode(true);
(%i14)
 

Re: 奇数の完全数はない

 投稿者:うんざりはちべえ  投稿日:2017年10月12日(木)13時29分12秒
返信・引用
  1+x+x^2+x^3+x^4+・・・
において、x=30k+Pだから、
1+(30k+P)+(30k+P)^2+(30k+P)^3+(30k+P)^4+・・・
であるから、
     1
     (30k+P)
     (30k+P)^2
     (30k+P)^3
     (30k+P)^4
        ・
        ・
+)_______________
であるから、2項定理の和と考えられないか?
 

Re: 奇数の完全数はない

 投稿者:うんざりはちべえ  投稿日:2017年10月 9日(月)16時27分51秒
返信・引用
  (%i15) x:210*n+11;
(%o15)                            210 n + 11
(%i16) factor(1+x+x^2);
                                    2
(%o16)                     7 (6300 n  + 690 n + 19)
(%i17) factor(1+x+x^2+x^3+x^4);
                       4             3            2
(%o17)   5 (388962000 n  + 83349000 n  + 6703200 n  + 239820 n + 3221)

3221は
(%i29) factor(3221);
(%o29)                               3221
素数

(%i18) factor(1+x+x^2+x^3+x^4+x^5+x^6);
                       6                   5                  4
(%o18) 85766121000000 n  + 27363476700000 n  + 3638739510000 n
                                     3                2
                     + 258150375000 n  + 10305508500 n  + 219496410 n + 1948717
(%i19) factor(1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^10);
                                 10                            9
(%o19) 166798809782010000000000 n   + 88165085170491000000000 n
                            8                           7
+ 20972775515674500000000 n  + 2956757003332650000000 n
                          6                         5                       4
+ 273583634055480000000 n  + 17360190919096200000 n  + 765075733313220000 n
                      3                    2
+ 23123150131410000 n  + 458680010386500 n  + 5392390574550 n + 28531167061

28531167061は
(%i30) factor(28531167061);
(%o30)                           15797 1806113
の2つの素数の積

(%i20) factor(1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^10+x^11+x^12);
                                     12                                 11
(%o20) 7355827511386641000000000000 n   + 4658690757211539300000000000 n
                                 10                                9
+ 1352404749712537080000000000 n   + 237955182035015466000000000 n
                               8                              7
+ 28262961454640125500000000 n  + 2387308406271710670000000 n
                             6                           5
+ 147047541606050526000000 n  + 6654963909912897600000 n
                          4                        3                      2
+ 219630905796058470000 n  + 5154807238223895000 n  + 81671350178577600 n
+ 784293251342580 n + 3452271214393

3452271214393は、
(%i31) factor(3452271214393);
(%o31)                          1093 3158528101
の2つの素数の積

(%i21) factor(1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^10+x^11+x^12+x^13+x^14+x^15+x^16);
                                               16
(%o21) 14305686902419853283210000000000000000 n
                                           15
+ 12057650389182447767277000000000000000 n
                                          14
+ 4764020812901087648916600000000000000 n
                                          13
+ 1171240462493551577194200000000000000 n
                                         12
+ 200544720657388320506580000000000000 n
                                        11
+ 25358332225871077799914800000000000 n
                                       10
+ 2449497409383685863202560000000000 n
                                      9                                     8
+ 184378682370596954106888000000000 n  + 10929798325557866384343000000000 n
                                   7                                  6
+ 511948133993941426133100000000 n  + 18884610496204512526908000000 n
                                5                               4
+ 542835935758890179985600000 n  + 11920036689321926732280000 n
                             3                           2
+ 193300517722953519900000 n  + 2183151451258349208000 n
+ 15342614801446744560 n + 50544702849929377

50544702849929377は、
(%i32) factor(50544702849929377);
(%o32)                         50544702849929377
より素数

(%i22) factor(1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^10+x^11+x^12+x^13+x^14+x^15+x^16+x^17+x^18);
                                                   18
(%o22) 630880792396715529789561000000000000000000 n
                                               17
+ 597834655652125668705345900000000000000000 n
                                               16
+ 267530650762153676249310210000000000000000 n
                                              15
+ 75120456248659725672099429000000000000000 n
                                              14
+ 14831599636072064826496290600000000000000 n
                                             13
+ 2186539156559768312557140480000000000000 n
                                            12
+ 249444241836888912784135452000000000000 n
                                           11
+ 22516136123226354777899278800000000000 n
                                          10
+ 1630222805244685824970858620000000000 n
                                        9
+ 95382401540052391035067818000000000 n
                                       8                                      7
+ 4520517299327130223677067800000000 n  + 173131689472698817373785020000000 n
                                    6                                   5
+ 5318613511245915616182888000000 n  + 129278270563075263508981200000 n
                                 4                               3
+ 2431649810288491596616680000 n  + 34152131662034750683956000 n
                             2
+ 337273227380626099560900 n  + 2089972918141729813710 n + 6115909044841454629

6115909044841454629は、
(%i33) factor(6115909044841454629);
(%o33)                        6115909044841454629
より素数

(%i23) factor(1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^10+x^11+x^12+x^13+x^14+x^15+x^16+x^17+x^18+x^19+x^20+x^21+x^22);
                                                             22
(%o23) 1226943273861056329490036128410000000000000000000000 n
                                                         21
+ 1419748645467793752695613234303000000000000000000000 n
                                                        20
+ 784102999710343549524210616938300000000000000000000 n
                                                        19
+ 274955457209404420212727110447510000000000000000000 n
                                                       18
+ 68698088899536524336702653810545000000000000000000 n
                                                       17
+ 13009007228676552316766899190790900000000000000000 n
                                                      16
+ 1938863361708725639934149633764170000000000000000 n
                                                     15
+ 233121853951436805330535011300177000000000000000 n
                                                    14
+ 22993583027971437419919753920738400000000000000 n
                                                   13
+ 1881582241648830607606749541186500000000000000 n
                                                  12
+ 128678595200393997090560001893406000000000000 n
                                                11
+ 7384879963505582701948531554355800000000000 n
                                               10
+ 356133112570963992003872830718580000000000 n
                                              9
+ 14412372532849525770923431939146000000000 n
                                            8
+ 487444892891332003316233386093000000000 n
                                           7
+ 13677572191466159875581765766740000000 n
                                         6
+ 314833636918089321994740761577000000 n
                                       5                                     4
+ 5846378095796530139576727446700000 n  + 85447100973255254440743320190000 n
                                   3                                 2
+ 946512280816690671168548715000 n  + 7470501257003997240867806100 n
+ 37437124443007606136016330 n + 89543024325523737224653

89543024325523737224653は、
(%i34) factor(89543024325523737224653);
(%o34)                    829 28878847 3740221981231
の3つの素数の積

(%i24) factor(1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^10+x^11+x^12+x^13+x^14+x^15+x^16+x^17+x^18+x^19+x^20+x^21+x^22+x^23+x^24+x^25+x^26+x^27+x^28);
                                                                           28
(%o24) 105230165286103494342858306883583597610000000000000000000000000000 n
                                                                       27
+ 154838671778123713104491508700130150769000000000000000000000000000 n
                                                                       26
+ 109849793403878922121719388110944546475600000000000000000000000000 n
                                                                      25
+ 50031358815846701370258094272260372401140000000000000000000000000 n
                                                                      24
+ 16433052185724117403943597506248708850131000000000000000000000000 n
                                                                     23
+ 4145342188294979483467323090335453593069500000000000000000000000 n
                                                                    22
+ 835108530298067237407978906298062824230700000000000000000000000 n
                                                                    21
+ 137936302415746750977521725907299163996280000000000000000000000 n
                                                                   20
+ 19029352753699056640540243958638405878094500000000000000000000 n
                                                                  19
+ 2222454002563376321200483271507040228979050000000000000000000 n
                                                                 18
+ 221928383044750584815058310999958972113560000000000000000000 n
                                                                17
+ 19086415066703403771622494997194106594119000000000000000000 n
                                                               16
+ 1421114280463355842239213763858575643984350000000000000000 n
                                                             15
+ 91928020428888425753597513340554909802015000000000000000 n
                                                            14
+ 5176768655746522159115991942412841353281000000000000000 n
                                                           13
+ 253950196482641643680500788557091536562600000000000000 n
                                                          12
+ 10845020524775390666101469101096712511315000000000000 n
                                                        11
+ 402370967846740143239056686452477707543500000000000 n
                                                       10
+ 12924575128254440709755918133039411971400000000000 n
                                                     9
+ 357550754846817910770850145434726037310000000000 n
                                                   8
+ 8457282737500029781363313149236996670500000000 n
                                                  7
+ 169351027629007707007410446465462028450000000 n
                                                6
+ 2832403961166700236398987832721036530000000 n
                                              5
+ 38839743667603131026527225390001832000000 n
                                            4
+ 425342385445770737258151127971671550000 n
                                          3
+ 3577404383834385826638263287130211000 n
                                        2
+ 21698575567252209399332699811014400 n  + 84492601564797901222674405945060 n
+ 158630929717149157441443670489

158630929717149157441443670489は、
(%i35) factor(158630929717149157441443670489);
(%o35)                  523 303309617049998388989376043
の2つの素数の積

(%i25) factor(1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^10+x^11+x^12+x^13+x^14+x^15+x^16+x^17+x^18+x^19+x^20+x^21+x^22+x^23+x^24+x^25+x^26+x^27+x^28+x^29+x^30);
(%o25) 4640650289117164100520051333566036654601000000000000000000000000000000
  30
n   + 7314548789037053891772080911477895869871100000000000000000000000000000
  29
n   + 5572463402725610542926061641020169411437550000000000000000000000000000
  28
n   + 2732624448589913119916369003031961975850595000000000000000000000000000
  27
n   + 969134304121514687421233091524835270907591500000000000000000000000000
  26
n   + 264784086018571468492929598169606043402508110000000000000000000000000
  25                                                                         24
n   + 57968166410540188589188077743350459919420811000000000000000000000000 n
                                                                         23
+ 10442778751295194872433116753539533264943191500000000000000000000000 n
                                                                        22
+ 1577508305764944523090340579929741438618695750000000000000000000000 n
                                                                       21
+ 202616123827439894312517368197153108098322575000000000000000000000 n
                                                                      20
+ 22357330867313885247795673748455963639340641500000000000000000000 n
                                                                     19
+ 2135936968418536343039379902048422419671760150000000000000000000 n
                                                                    18
+ 177703711725018538830267309504194993990280375000000000000000000 n
                                                                   17
+ 12929029899725795423245139822005577895364957500000000000000000 n
                                                                 16
+ 824957780035952211109580621720657639887107750000000000000000 n
                                                                15
+ 46239165326328928377611266663522207900612695000000000000000 n
                                                               14
+ 2277904320237728303432023455524081724415204500000000000000 n
                                                             13
+ 98576528280903184079571782535029154629018250000000000000 n
                                                            12
+ 3741175118105782567662955642310187290658825000000000000 n
                                                           11
+ 124166412490735743275992692249063304166002500000000000 n
                                                         10
+ 3588724246634837386999915875887554694080650000000000 n
                                                       9
+ 89804667902154344672198175036203650586865000000000 n
                                                      8
+ 1930641973570970690344392517151108879542500000000 n
                                                    7
+ 35290013339441385718329838449191175002250000000 n
                                                  6
+ 540918094243655683459917773804604599325000000 n
                                                5
+ 6822454337866536075297199894381786538100000 n
                                              4
+ 68950944074768944161815634932779567410000 n
                                            3
+ 536839473293673479892066872171819205000 n
                                          2
+ 3022879086867409918811180098467484500 n
+ 10956479684633775155323072877011650 n + 19194342495775048050414684129181

19194342495775048050414684129181は、
(%i36) factor(19194342495775048050414684129181);
(%o36)                50159 2428541 157571957584602258799
の3つの素数の積

(%i26) factor(1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^10+x^11+x^12+x^13+x^14+x^15+x^16+x^17+x^18+x^19+x^20+x^21+x^22+x^23+x^24+x^25+x^26+x^27+x^28+x^29+x^30+x^31+x^32+x^33+x^34+x^35+x^36);
(%o26) 39801057421510767942205888560083606120894457272100000000000000000000000\
               36
0000000000000 n   + 7524295141114178510978922742072948395235761684297000000000\
                            35
00000000000000000000000000 n   + 691473427529811563868491237623438903981507877\
                                         34
178960000000000000000000000000000000000 n   + 41153588550019962821710436145521\
                                                      33
8861859313533576310000000000000000000000000000000000 n   + 1782949978908474896\
                                                                   32
37278101707373653467704595837254500000000000000000000000000000000 n   + 599238\
34357057279565924618854005055378601048577164370000000000000000000000000000000
  31
n   + 16258986830500890198434302895455575419584793938393254000000000000000000\
              30
000000000000 n   + 36593431023044087609740820475300746225124722989377732000000\
                         29
00000000000000000000000 n   + 696627464318691603191532049462393187546866824520\
                                   28
779000000000000000000000000000000 n   + 11381738285572422057190248926749162619\
                                             27
0334119991977220000000000000000000000000000 n   + 1613867544952291177417374023\
                                                      26
4803186507115973199033025600000000000000000000000000 n   + 2003305322581458834\
                                                              25
199862239012927775550889721505255120000000000000000000000000 n   + 21918336230\
                                                                     24
3146603617430262138185517131624525776469476000000000000000000000000 n   + 2125\
                                                                           23
1043117442570860283224558509158170980138747659074000000000000000000000000 n
+ 1833529704014434043977633721328779144800472240101914000000000000000000000000
  22
n
+ 141231121065702059936134203364126474791555503529828960000000000000000000000
  21
n
+ 9735178271635940842582347771465282633684422607469227000000000000000000000
  20
n   + 601509301482497213079831779009740465927691965793765100000000000000000000
  19
n   + 33346019564187511266757057244778838130383399154824800000000000000000000
  18
n   + 1659153906384446049995475685090136219034617461674090000000000000000000
  17                                                                         16
n   + 74068337977788894520613235325310932297238765297789100000000000000000 n
                                                                        15
+ 2963899937918360601400472524022570917394526959229270000000000000000 n
                                                                       14
+ 106136713476131521747411799681074711983523807277706000000000000000 n
                                                                     13
+ 3393146759948831430995374740205631662354204390602000000000000000 n
                                                                   12
+ 96532793148683529712053763889589331663368983289300000000000000 n
                                                                  11
+ 2433658054127809554370555831197261673188763015011600000000000 n
                                                                10
+ 54078631136670799231144625494222504814523903801120000000000 n
                                                               9
+ 1051991162533148780419801145573582303612959014216000000000 n
                                                             8
+ 17760292960726002343109966915020948377869822946000000000 n
                                                           7
+ 257335131951753333828651467007863195824904860200000000 n
                                                         6
+ 3153815367306745003692522731691885936810793512000000 n
                                                       5
+ 32061930861334967462063120718579973591562150400000 n
                                                     4
+ 263134035061539496889610362661273332568876570000 n
                                                   3
+ 1675305056641466473414222463774101916791425000 n
                                                2
+ 7764447849969202777111171950621642778812000 n
+ 23305069853731200100034140779119451088860 n
+ 34003948586157739899240688230576198697

34003948586157739899240688230576198697は、
(%i37) factor(34003948586157739899240688230576198697);
(%o37)            2591 36855109 136151713 2615418118891695851
の4つの素数の積

(%i27) factor(1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^10+x^11+x^12+x^13+x^14+x^15+x^16+x^17+x^18+x^19+x^20+x^21+x^22+x^23+x^24+x^25+x^26+x^27+x^28+x^29+x^30+x^31+x^32+x^33+x^34+x^35+x^36+x^37+x^38+x^39+x^40);
(%o27) 77405494483928356601681434130536198019976749447352801000000000000000000\
                        40
0000000000000000000000 n   + 1625515384162495488635310116741260158419511738394\
                                               39
408821000000000000000000000000000000000000000 n   + 16641303700728452356928382\
                                                                      38
69822253273078003540839800241000000000000000000000000000000000000000 n   + 110\
665869014709605400565683317631600779157688620316610760000000000000000000000000\
               37
0000000000000 n   + 5374298853218876295474212210056291574827745353033882688700\
                                     36
00000000000000000000000000000000000 n   + 203152922319639893546363683672651356\
                                                           35
409049092238285281519800000000000000000000000000000000000 n   + 62217280970326\
779673617572014832090596577063900736307667280000000000000000000000000000000000
  34
n   + 15865927719850113591069979173698900275796604412540022954460000000000000\
                       33
000000000000000000000 n   + 34360969621671433364285437458039742683074846242034\
                                           32
43333004500000000000000000000000000000000 n   + 641432996886112975089524911432\
                                                              31
272241882614682597892893942650000000000000000000000000000000 n   + 10439840249\
8960188630308690018652690396531326259130640543358000000000000000000000000000000
  30
n   + 14948779683789330025791701712613668018873326539866506165950800000000000\
                    29
000000000000000000 n   + 18967420867378648462158592641493133747937775454709826\
                                     28
82750400000000000000000000000000000 n   + 214492064562905666367666113129816586\
                                                     27
12553801228312830515916000000000000000000000000000
 

Re: 奇数の完全数はない

 投稿者:うんざりはちべえ  投稿日:2017年10月 9日(月)16時26分14秒
返信・引用
  (%i1) x:210*n+1;
(%o1)                              210 n + 1
(%i2) factor(1+x+x^2);
                                     2
(%o2)                      3 (14700 n  + 210 n + 1)
(%i3) factor(1+x+x^2+x^3+x^4);
                           4            3          2
(%o3)        5 (388962000 n  + 9261000 n  + 88200 n  + 420 n + 1)
(%i4) factor(1+x+x^2+x^3+x^4+x^5+x^6);
                         6                 5               4             3
(%o4) 7 (12252303000000 n  + 408410100000 n  + 5834430000 n  + 46305000 n
                                                                 2
                                                       + 220500 n  + 630 n + 1)
(%i5) factor(1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^10);
                                10                           9
(%o5) 166798809782010000000000 n   + 8737080512391000000000 n
                          8                        7                      6
+ 208025726485500000000 n  + 2971796092650000000 n  + 28302819930000000 n
                    5                 4               3            2
+ 188685466200000 n  + 898502220000 n  + 3056130000 n  + 7276500 n  + 11550 n
+ 11
(%i6) factor(1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^10+x^11+x^12);
                                    12                                11
(%o6) 7355827511386641000000000000 n   + 455360750704887300000000000 n
                               10                             9
+ 13010307162996780000000000 n   + 227164093322166000000000 n
                           8                         7                       6
+ 2704334444311500000000 n  + 23180009522670000000 n  + 147174663636000000 n
                    5                  4               3             2
+ 700831731600000 n  + 2502970470000 n  + 6621615000 n  + 12612600 n
+ 16380 n + 13
(%i7) factor(1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^10+x^11+x^12+x^13+x^14+x^15+x^16);
                                              16
(%o7) 14305686902419853283210000000000000000 n
                                          15
+ 1158079415910178599117000000000000000 n
                                        14
+ 44117311082292518061600000000000000 n
                                       13
+ 1050412168626012334800000000000000 n
                                     12                                   11
+ 17506869477100205580000000000000 n   + 216751717335526354800000000000 n
                                 10                               9
+ 2064302069862155760000000000 n   + 15447158345907288000000000 n
                            8                          7
+ 91947371106591000000000 n  + 437844624317100000000 n
                        6                     5                   4
+ 1667979521208000000 n  + 5054483397600000 n  + 12034484280000 n
                3             2
+ 22041180000 n  + 29988000 n  + 28560 n + 17
(%i8) factor(1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^10+x^11+x^12+x^13+x^14+x^15+x^16+x^17+x^18);
                                                  18
(%o8) 630880792396715529789561000000000000000000 n
                                              17
+ 57079690740655214600007900000000000000000 n
                                             16
+ 2446272460313794911428910000000000000000 n
                                           15
+ 66010526706880180149669000000000000000 n
                                          14
+ 1257343365845336764755600000000000000 n
                                        13
+ 17962048083504810925080000000000000 n
                                      12                                    11
+ 199578312038942343612000000000000 n   + 1764978269732143174800000000000 n
                                  10                               9
+ 12606987640943879820000000000 n   + 73374002143059618000000000 n
                             8                           7
+ 349400010205045800000000 n  + 1361298741058620000000 n
                        6                      5                   4
+ 4321583304948000000 n  + 11080982833200000 n  + 22614250680000 n
                3             2
+ 35895636000 n  + 42732900 n  + 35910 n + 19
(%i9) factor(1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^10+x^11+x^12+x^13+x^14+x^15+x^16+x^17+x^18+x^19+x^20+x^21+x^22);
                                                            22
(%o9) 1226943273861056329490036128410000000000000000000000 n
                                                        21
+ 134379501422877597991765861683000000000000000000000 n
                                                      20
+ 7038926265007874180521068945300000000000000000000 n
                                                     19
+ 234630875500262472684035631510000000000000000000 n
                                                   18
+ 5586449416672916016286562655000000000000000000 n
                                                  17
+ 101088132301700385056613990900000000000000000 n
                                                16
+ 1444116175738576929380199870000000000000000 n
                                              15
+ 16700663256840685577866257000000000000000 n
                                            14
+ 159053935779435100741583400000000000000 n
                                          13
+ 1262332823646310323345900000000000000 n
                                       12
+ 8415552157642068822306000000000000 n
                                     11                                   10
+ 47360250237812508523800000000000 n   + 225525001132440516780000000000 n
                                9                              8
+ 908708795771738346000000000 n  + 3090846244121559000000000 n
                           7                         6                      5
+ 8830989268918740000000 n  + 21026164925997000000 n  + 41227774364700000 n
                   4                3             2
+ 65440911690000 n  + 82006155000 n  + 78101100 n  + 53130 n + 23
(%i10) factor(1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^10+x^11+x^12+x^13+x^14+x^15+x^16+x^17+x^18+x^19+x^20+x^21+x^22+x^23+x^24+x^25+x^26+x^27+x^28);
                                                                           28
(%o10) 105230165286103494342858306883583597610000000000000000000000000000 n
                                                                      27
+ 14531784729985720647347099522018687289000000000000000000000000000 n
                                                                    26
+ 968785648665714709823139968134579152600000000000000000000000000 n
                                                                   25
+ 41519384942816344706705998634339106540000000000000000000000000 n
                                                                  24
+ 1285123819658601145683757100586686631000000000000000000000000 n
                                                                23
+ 30598186182347646325803740490159205500000000000000000000000 n
                                                              22
+ 582822593949478977634356961717318200000000000000000000000 n
                                                            21
+ 9118992966556473799721231373808380000000000000000000000 n
                                                           20
+ 119415384085858585472539934657014500000000000000000000 n
                                                         19
+ 1326837600953984283028221496189050000000000000000000 n
                                                       18
+ 12636548580514136028840204725610000000000000000000 n
                                                     17
+ 103936979666566486817300385189000000000000000000 n
                                                  16
+ 742406997618332048695002751350000000000000000 n
                                                15
+ 4623047237916353416782068415000000000000000 n
                                              14
+ 25159440750565188662759556000000000000000 n
                                            13
+ 119806860716977088870283600000000000000 n
                                         12
+ 499195252987404536959515000000000000 n
                                       11                                    10
+ 1817797840010156577163500000000000 n   + 5770786793683036752900000000000 n
                                  9                               8
+ 15909437275817895810000000000 n  + 37879612561471180500000000 n
                            7                          6
+ 77305331758104450000000 n  + 133862046334380000000 n
                       5                    4                 3              2
+ 194002965702000000 n  + 230955911550000 n  + 219958011000 n  + 161141400 n
+ 85260 n + 29
(%i11) factor(1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^10+x^11+x^12+x^13+x^14+x^15+x^16+x^17+x^18+x^19+x^20+x^21+x^22+x^23+x^24+x^25+x^26+x^27+x^28+x^29+x^30);
(%o11) 4640650289117164100520051333566036654601000000000000000000000000000000
  30
n   + 685048376012533748172007577812129220441100000000000000000000000000000
  29                                                                         28
n   + 48932026858038124869429112700866372888650000000000000000000000000000 n
                                                                        27
+ 2252426633147786700338800425912896529795000000000000000000000000000 n
                                                                      26
+ 75080887771592890011293347530429884326500000000000000000000000000 n
                                                                     25
+ 1930651399840960028861828936496768454110000000000000000000000000 n
                                                                   24
+ 39838838409416635516196470118187285561000000000000000000000000 n
                                                                 23
+ 677531265466269311499939967996382407500000000000000000000000 n
                                                               22
+ 9679018078089561592856285257091177250000000000000000000000 n
                                                              21
+ 117786992484687786579732571911691575000000000000000000000 n
                                                            20
+ 1233958968887205383216245991455816500000000000000000000 n
                                                          19
+ 11217808808065503483784054467780150000000000000000000 n
                                                       18
+ 89030228635440503839555987839525000000000000000000 n
                                                     17
+ 619624301858377132949290757857500000000000000000 n
                                                   16
+ 3793618174643125303771167905250000000000000000 n
                                                 15
+ 20473494910772422274320588695000000000000000 n
                                              14
+ 97492832908440106068193279500000000000000 n
                                            13
+ 409633751716134899446190250000000000000 n
                                          12
+ 1517162043393092220171075000000000000 n
                                       11
+ 4943134477220601218602500000000000 n
                                     10                                  9
+ 14123241363487432053150000000000 n   + 35228039682168197865000000000 n
                               8                             7
+ 76251168143221207500000000 n  + 142082922006002250000000 n
                          6                       5                    4
+ 225528447628575000000 n  + 300704596838100000 n  + 330444611910000 n
                 3              2
+ 291397365000 n  + 198229500 n  + 97650 n + 31
(%i12) factor(1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^10+x^11+x^12+x^13+x^14+x^15+x^16+x^17+x^18+x^19+x^20+x^21+x^22+x^23+x^24+x^25+x^26+x^27+x^28+x^29+x^30+x^31+x^32+x^33+x^34+x^35+x^36);
(%o12) 39801057421510767942205888560083606120894457272100000000000000000000000\
               36
0000000000000 n   + 7012567259980468637436275603443302030824261519370000000000\
                           35
0000000000000000000000000 n   + 6010771937126115974945379088665687454992224159\
                                      34
460000000000000000000000000000000000 n   + 33393177428478422083029883825920485\
                                                33
8610679119970000000000000000000000000000000000 n   + 1351628610200317084313114\
                                                         32
3453348768086622726284500000000000000000000000000000000 n   + 4247975632058139\
                                                                31
40784121651390961282722428540370000000000000000000000000000000 n   + 107885095\
                                                                      30
41734957226263407019452984958029931184000000000000000000000000000000 n
+ 227512786254274608172901780682341859659134603200000000000000000000000000000
  29
n
+ 4062728325969189431658960369327533208198832200000000000000000000000000000
  28
n   + 62338159498998144718576640587565324358606420000000000000000000000000000
  27
n   + 831175459986641929581021874500870991448085600000000000000000000000000
  26                                                                        25
n   + 9715037843999710865232723208451738861081520000000000000000000000000 n
                                                                       24
+ 100234517438092254958750318817359210471476000000000000000000000000 n
                                                                    23
+ 917898511337841162625918670488637458530000000000000000000000000 n
                                                                  22
+ 7493049072145642143885050371335815988000000000000000000000000 n
                                                                21
+ 54711151955349133114081320171658338960000000000000000000000 n
                                                              20
+ 358227780660024085866008643981096267000000000000000000000 n
                                                            19
+ 2107222239176612269800050846947625100000000000000000000 n
                                                          18
+ 11149324016807472326984396015595900000000000000000000 n
                                                       17
+ 53092019127654630128497123883790000000000000000000 n
                                                     16
+ 227537224832805557693559102359100000000000000000 n
                                                  15
+ 877127624072039564805103115670000000000000000 n
                                                14
+ 3037671425357712778545811656000000000000000 n
                                             13
+ 9433762190551903038962148000000000000000 n
                                           12
+ 26204894973755286219339300000000000000 n
                                        11
+ 64888311363584518257411600000000000 n
                                      10                                   9
+ 142611673326559380785520000000000 n   + 276671676647646065016000000000 n
                                8                             7
+ 470530062325928682000000000 n  + 695364624126988200000000 n
                          6                       5                    4
+ 883002697304112000000 n  + 949465265918400000 n  + 847736844570000 n
                 3              2
+ 611642745000 n  + 342657000 n  + 139860 n + 37
(%i13) factor(1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^10+x^11+x^12+x^13+x^14+x^15+x^16+x^17+x^18+x^19+x^20+x^21+x^22+x^23+x^24+x^25+x^26+x^27+x^28+x^29+x^30+x^31+x^32+x^33+x^34+x^35+x^36+x^37+x^38+x^39+x^40);
(%o13) 77405494483928356601681434130536198019976749447352801000000000000000000\
                        40
0000000000000000000000 n   + 1511250130400506009842351809215230532770974632067\
                                              39
36421000000000000000000000000000000000000000 n   + 143928583847667239032604934\
                                                                   38
21097433645437853638736802000000000000000000000000000000000000000 n   + 890986\
471437940051154221021306031606622343320493230600000000000000000000000000000000\
        37
000000 n   + 40306530850763954695071903344796667918629816879455670000000000000\
                          36
000000000000000000000000 n   + 14203253728364441178263432607214063933231459281\
                                           35
33199800000000000000000000000000000000000 n   + 405807249381841176521812360206\
                                                          34
11611237804169375234280000000000000000000000000000000000 n   + 966207736623431\
                                                                       33
372670981810014562172328670699410340000000000000000000000000000000000 n   + 19\
554204193569444446912727107437567773318335583304500000000000000000000000000000\
     32
000 n   + 34142261290359347446990475901875118334365347843865000000000000000000\
               31
0000000000000 n   + 5202630291864281515731882042190494222379481576208000000000\
                       30
000000000000000000000 n   + 69818848072637544150514434332426545841456246260800\
                             29
000000000000000000000000000 n
+ 831176762769494573220409932528887450493526741200000000000000000000000000000
  28
n
+ 8829350227221737224685673275947888668246254760000000000000000000000000000
  27
n   + 84089049783064164044625459770932273030916712000000000000000000000000000
  26
n   + 720763283854835691811075369465133768836428960000000000000000000000000
  25                                                                        24
n   + 5577334934590990472347607025623058925519986000000000000000000000000 n
                                                                      23
+ 39056967329068560730725539395119460262745000000000000000000000000 n
                                                                    22
+ 247980744946467052258574853302345779446000000000000000000000000 n
                                                                  21
+ 1429462940794170977931634492720288954200000000000000000000000 n
                                                               20
+ 7487663023207562265356180676153894522000000000000000000000 n
                                                             19
+ 35655538205750296501696098457875688200000000000000000000 n
                                                           18
+ 154352979245672279228121638345782200000000000000000000 n
                                                        17
+ 607185632643431326156172076308460000000000000000000 n
                                                      16
+ 2168520116583683307700614558244500000000000000000 n
                                                   15
+ 7021874663223355472554370950506000000000000000 n
                                                 14
+ 20576922090031810908584237217600000000000000 n
                                              13
+ 54436301825480981239640839200000000000000 n
                                            12
+ 129610242441621383903906760000000000000 n
                                         11
+ 276672110302311656937732000000000000 n
                                      10                                   9
+ 526994495813926965595680000000000 n   + 890466890008171524048000000000 n
                                 8                              7
+ 1325099538702636196500000000 n  + 1720908491821605450000000 n
                           6                        5                     4
+ 1928188786354740000000 n  + 1836370272718800000 n  + 1457436724380000 n
                 3              2
+ 937861470000 n  + 470106000 n  + 172200 n + 41
(%i14) factor(1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^10+x^11+x^12+x^13+x^14+x^15+x^16+x^17+x^18+x^19+x^20+x^21+x^22+x^23+x^24+x^25+x^26+x^27+x^28+x^29+x^30+x^31+x^32+x^33+x^34+x^35+x^36+x^37+x^38+x^39+x^40+x^41+x^42);
(%o14) 34135823067412405261341512451566463326809746506282585241000000000000000\
                             42
000000000000000000000000000 n   + 69897161518987306011318335019874186812039004\
                                                       41
75095957930300000000000000000000000000000000000000000 n   + 698971615189873060\
113183350198741868120390047509595793030000000000000000000000000000000000000000
  40
n   + 45488628925055230896254789457378439036406336425227662721000000000000000\
                          39
000000000000000000000000 n   + 21661251869073919474407042598751637636383969726\
                                                 38
29888701000000000000000000000000000000000000000 n   + 804560783708459866192261\
                                                                      37
58223934654077997601840538723180000000000000000000000000000000000000 n   + 242\
645315721599007264332858135675940870151497614323133400000000000000000000000000\
            36
0000000000 n   + 6107399103196709706653276021102047491289527490972759140000000\
                              35
0000000000000000000000000000 n   + 1308728379256437794282844861664724462419184\
                                               34
462351305530000000000000000000000000000000000 n   + 24235710726971070264497127\
                                                              33
067865267822577490043542695000000000000000000000000000000000 n   + 39238769748\
                                      &
 

Re: 奇数の完全数はない

 投稿者:うんざりはちべえ  投稿日:2017年10月 9日(月)15時15分25秒
返信・引用
  1+x+x^2+・・+x^mは、1が並んだ数でm+1が素数だから、とりあえずできるところまで、やってみよう。一般解は、それをやっていると何かしらめどがたつかもしれない・・・  

Re: 奇数の完全数はない

 投稿者:うんざりはちべえ  投稿日:2017年10月 8日(日)01時04分17秒
返信・引用
  mが偶数ならば、x^m-1は合成数であるとしかならないなあ。  

Re: 奇数の完全数はない

 投稿者:うんざりはちべえ  投稿日:2017年10月 8日(日)00時47分55秒
返信・引用 編集済
  >また、
>                   x^(m+1)-1
>1+x+x^2+・・+x^m=-------------
>                     x-1
>なので、m+1=30k+Pとして考えれば、どうかな?
より、
                      x^m-1
1+x+x^2+・・+x^(m-1)=-------------
                       x-1
なので、
                   x^(m+1)-1     x^m-1
1+x+x^2+・・+x^m=-------------=--------+x^m
                     x-1          x-1
ここで
m+1=30k+P
m=30k+P-1
より、P-1は偶数。
P=1なら
                   x^(m+1)-1     x^m-1       (x^15k+1)(x^15k-1)
1+x+x^2+・・+x^m=-------------=--------+x^m=-------------------+x^30k
                     x-1          x-1          x-1
ここでk=2qなら
                   x^m-1       (x^30q+1)(x^30q-1)       (x^30q+1)(x^15q+1)(x^15q-1)
1+x+x^2+・・+x^m=--------+x^m=-------------------+x^60q=---------------------------+x^60q
                    x-1          x-1            x-1

P=7なら
                   x^(m+1)-1     x^m-1       {x^(15k+3)+1}{x^(15k+3)-1}
1+x+x^2+・・+x^m=-------------=--------+x^m=---------------------------+x^30k
                     x-1          x-1          x-1
kが奇数ならk=2q+1で・・・・
 

Re: 奇数の完全数はない

 投稿者:うんざりはちべえ  投稿日:2017年10月 8日(日)00時23分34秒
返信・引用
  > 30k+PのPは1,7,11,13,17,19,23,29である。kは自然数である。
であるから、Pが奇数なんだな。30kは偶数なんだけどね。
 

Re: 奇数の完全数はない

 投稿者:うんざりはちべえ  投稿日:2017年10月 8日(日)00時12分4秒
返信・引用
  x^a-1において、a=2nならば、x^2n-1=(x^n+1)(x^n-1)です。
a=p+2mなら、x^a-1=x^p x^2m-1です。ここで、x^p=x^2qとすると、つまり、pが偶数であればという事ですが、
x^a-1=x^2q x^2m-1=(x^q x^m +1)(x^q x^m-1)
のはずですよね。
例えば、a=6=2+4として、
x^a-1=x^2 x^4-1=(x x^2 +1)(x x^2-1)=(x^3+1)(x^3-1)
と間違っていませんよね。
 

第2の人生

 投稿者:うんざりはちべえ  投稿日:2017年10月 7日(土)23時47分8秒
返信・引用
  第2の人生は墓守として勤めを果たすという事なのかな。  

BS1スペシャル「爆走風塵(じん) 中国・激変するトラック業界」

 投稿者:うんざりはちべえ  投稿日:2017年10月 7日(土)23時42分44秒
返信・引用
  中国のトラック野郎の哀しい話でした。
自分を振り返って見れば、63まで仕事はあったし、技術者として、40年もやってこれたという事は、非常に幸せな人生だったのでしょうね。
 

占い

 投稿者:うんざりはちべえ  投稿日:2017年10月 7日(土)23時37分19秒
返信・引用
  先週だったか占いをみていたら、あなたは不思議運の最中であるとのことでした。
不思議運というのは過大評価という事で、そのうち本当がバレて評価が下がるという事でした。

まあ、自分の実力として、ないものはないのです。諦めるしかありません。
 

Re: 奇数の完全数はない

 投稿者:うんざりはちべえ  投稿日:2017年 9月15日(金)08時47分40秒
返信・引用
  したがって、前回1+x+x^2+・・+x^mを2から26までやりましたが、m+1が素数の場合だけ考えれば、合成数なので、それぞれの素因数分解した構成には変更がない。
なので、m+1が素数の場合を考えればよい。

また、
                   x^(m+1)-1
1+x+x^2+・・+x^m=-------------
                     x-1
なので、m+1=30k+Pとして考えれば、どうかな?
30k+PのPは1,7,11,13,17,19,23,29である。kは自然数である。
すると、
x^(m+1)-1     x^(30k+1)-1
-------------=-------------
   x-1            x-1
あるいは、
x^(m+1)-1     x^(30k+7)-1
-------------=-------------
   x-1            x-1
あるいは、
x^(m+1)-1     x^(30k+11)-1
-------------=-------------
   x-1            x-1
あるいは、
x^(m+1)-1     x^(30k+13)-1
-------------=-------------
   x-1            x-1
あるいは、
x^(m+1)-1     x^(30k+17)-1
-------------=-------------
   x-1            x-1
あるいは、
x^(m+1)-1     x^(30k+19)-1
-------------=-------------
   x-1            x-1
あるいは、
x^(m+1)-1     x^(30k+23)-1
-------------=-------------
   x-1            x-1
あるいは、
x^(m+1)-1     x^(30k+29)-1
-------------=-------------
   x-1            x-1

を考えれば、どうかな・・・・
 

Re: 奇数の完全数はない

 投稿者:うんざりはちべえ  投稿日:2017年 9月12日(火)13時50分20秒
返信・引用
  >m+1が3で割り切れると1が3個並んだ数つまり、111で割れます。1+x+x^2で割れるということですね。

これは、例えば111111111は111 111 111の3つづつに区切れるから111で割ると、あまりが出ませんので、割り切れます。

111)111 111 111
      1 001 001
ですからね。
111 111 111=111 x(1 001 001)
x^8+x^7+x^6+ x^5+x^4+x^3 +x^2+x+1=(x^2+x+1)(x^6+ x^3+1)

では確認します。
(%i1) factor(1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8);
                            2            6    3
(%o1)                     (x  + x + 1) (x  + x  + 1)
 

Re: 奇数の完全数はない

 投稿者:うんざりはちべえ  投稿日:2017年 9月12日(火)12時08分40秒
返信・引用 編集済
  σ(x^m)=1+x+x^2+x^3+x^4+・・・+x^mですが、
1+x+x^2+x^3+x^4+・・・+x^mは、x進数の1がm+1並んだ数=11111・・・・111を10進数に変換する式でもあるわけです。
1が並んだ数は、次の特徴があります。
m+1が2で割り切れると1が2個並んだ数つまり、11で割れます。1+xで割れるということですね。
m+1が3で割り切れると1が3個並んだ数つまり、111で割れます。1+x+x^2で割れるということですね。
m+1が5で割り切れると1が5個並んだ数つまり、11111で割れます。1+x+x^2+x^3+x^4で割れるということですね。
m+1が7で割り切れると1が7個並んだ数つまり、1111111で割れます。1+x+x^2+x^3+x^4+x^5+x^6で割れるということですね。
このように、
m+1がpで割り切れると1がp個並んだ数つまり、11・・・111で割れます。1+x+x^2+x^3・・+x^pで割れるということですね。
したがって、pが素数でない限り、σ(x^m)は必ず合成数になります。

また、奇数の自然数aを素因数分解したものがa=x^m y^n z^p・・・ですから、xは素数です。
 

Re: 奇数の完全数はない

 投稿者:うんざりはちべえ  投稿日:2017年 9月10日(日)19時21分45秒
返信・引用
  たとえば、
(%i1) x:210*n+41;
(%o1)                             210 n + 41
(%i2) factor(1+x+x^2);
                                  2
(%o2)                      44100 n  + 17430 n + 1723

n=1723のとき、1723を因数に持つ。

(%i3) factor(1+x+x^2+x^3+x^4);
                    4              3             2
(%o3) 5 (388962000 n  + 305613000 n  + 90052200 n  + 11794020 n + 579281)

2つの合成数から成る。5とn=579281のとき579281を因数に持つ。

これの場合、
σ(x^4)=1+x+x^2+x^3+x^4
で、素数xがx=210n+41なら、
                    4              3             2
(%o3) 5 (388962000 n  + 305613000 n  + 90052200 n  + 11794020 n + 579281)

より、σ(x^4)を素因数分解したら、必ず5が出てきます。

x=210x1+41=251は素数ですが
(%i4) n:1;
(%o4)                                  1
(%i5) x:210*n+41;
(%o5)                                 251
(%i6) factor(x);
(%o6)                                 251
(%i7) factor(1+x+x^2+x^3+x^4);
                                     2
(%o7)                            5 11  6586781
このように、素因数分解したら5が出てきます。

また、
(%i8) factor(1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^10+x^11+x^12+x^13+x^14);
                2                               4              3             2
(%o8) 5 (44100 n  + 17430 n + 1723) (388962000 n  + 305613000 n  + 90052200 n
                                              8                        7
+ 11794020 n + 579281) (3782285936100000000 n  + 5889559529070000000 n
                        6                        5                       4
+ 4012224906501000000 n  + 1561872943587600000 n  + 379998835519590000 n
                      3                     2
+ 59169105663948000 n  + 5758164243833400 n  + 320207437100040 n
+ 7790284054561)
これも5が出てきます。
(%i8) factor(1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^10+x^11+x^12+x^13+x^14);
                      2
(%o8)             5 11  43 1471 6586781 2376251641 6603339961

もちろん、1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^10+x^11+x^12+x^13+x^14を因数分解すると、
(%i1) factor(1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^10+x^11+x^12+x^13+x^14);
        2            4    3    2            8    7    5    4    3
(%o1) (x  + x + 1) (x  + x  + x  + x + 1) (x  - x  + x  - x  + x  - x + 1)
ですから、1+x+x^2+x^3+x^4を含みますから、1+x+x^2+x^3+x^4と同じ素数構造を持ちますね。
 

Re: 奇数の完全数はない

 投稿者:うんざりはちべえ  投稿日:2017年 9月10日(日)19時07分8秒
返信・引用
  210n+Pは、2x3x5x7ですから、2,3,5,7の倍数は除かれていますので、もちろん、素数でないものもありますが、2,3,5,7以外のすべての素数は210n+Pに含まれます。

素数候補式は、2,3,5,7,11・・・の倍数を除いた式ですから、素数候補式に含まれない素数はありません。

 

ソフィージェルマン素数

 投稿者:うんざりはちべえ  投稿日:2017年 9月10日(日)19時00分9秒
返信・引用
  120000を超えました。510510まで、あと40万です。残り、4年くらいかな。  

Re: 奇数の完全数はない

 投稿者:うんざりはちべえ  投稿日:2017年 9月 9日(土)17時22分34秒
返信・引用
  詳しくは、数の不思議世界の掲示板の私の投稿をご覧ください。

これからは、ここの掲示板で進めます。
 

奇数の完全数はない

 投稿者:うんざりはちべえ  投稿日:2017年 9月 9日(土)17時16分26秒
返信・引用
  σ(x^m)=1+x+x^2+x^3+・・・・+x^m(mは偶数)に素数xに素数候補式x=210n+Pを代入すると、ある法則性があることがわかっています。
つまり、1+x+x^2+x^3+・・・・+x^m(mは偶数)が素因数分解できるのですが、その素数にある法則性があることがわかっています。ただし、mは26まで。
 

ホームページの復活

 投稿者:うんざりはちべえ  投稿日:2017年 9月 2日(土)20時19分6秒
返信・引用
  ホームページを復活しました。

最新の状態ではありません。
 

田口メソッド

 投稿者:うんざりはちべえ  投稿日:2017年 8月 5日(土)19時20分32秒
返信・引用
  戦後ノーベル物理学賞をもらった人はたくさんいるけど、工学的に見ればあまり価値がない。
その中で田口博士は、非常に大きな仕事をなされたと思う。
田口博士は、ロバスト設計といういかなる条件でも動作を全うする頑丈な設計の仕方を発明した。つまり、各パラメータの影響度を評価することで、影響を小さくすることができるようになった。
田口メソッドあるいは、品質工学という。したがって、設計段階で、ユーザー先で不具合を起こさないようにした。
これは、田口博士の実験計画法の改善によってなされたと言われている。

実験計画法は、総当たりの効率の悪い方法を直交表を使うことで、大幅に実験回数を減らすことができる。

さて、数式モデルにおいて、品質工学を適応すれば、影響の大きな、あるいは、小さなパラメータを見つけることができるので、効果的に評価してその対策を打つことができるだろう。
 

Re: 愛犬ベルの思い出

 投稿者:うんざりはちべえ  投稿日:2017年 7月30日(日)14時10分7秒
返信・引用
  もらってきてそんなに日がたってない頃。  

Re: 愛犬ベルの思い出

 投稿者:うんざりはちべえ  投稿日:2017年 7月30日(日)13時46分2秒
返信・引用
  2012年3月28日午後8:55分病死
2012年3月29日動物霊園に葬られる。
 

愛犬ベルの思い出

 投稿者:うんざりはちべえ  投稿日:2017年 7月30日(日)13時43分35秒
返信・引用
  ベルは2004年6月23日にやってきました。  

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