586 Paare "befreundeter Zahlen" im Bereich bis zu 1 Mrd: {{220,284}, {1184,1210}, {2620,2924}, {5020,5564}, {6232,6368}, {10744,10856}, {12285,14595}, {17296,18416}, {63020,76084}, {66928,66992}, {67095,71145}, {69615,87633}, {79750,88730}, {100485,124155}, {122265,139815}, {122368,123152}, {141664,153176}, {142310,168730}, {171856,176336}, {176272,180848}, {185368,203432}, {196724,202444}, {280540,365084}, {308620,389924}, {319550,430402}, {356408,399592}, {437456,455344}, {469028,486178}, {503056,514736}, {522405,525915}, {600392,669688}, {609928,686072}, {624184,691256}, {635624,712216}, {643336,652664}, {667964,783556}, {726104,796696}, {802725,863835}, {879712,901424}, {898216,980984}, {947835,1125765}, {998104,1043096}, {1077890,1099390}, {1154450,1189150}, {1156870,1292570}, {1175265,1438983}, {1185376,1286744}, {1280565,1340235}, {1328470,1483850}, {1358595,1486845}, {1392368,1464592}, {1466150,1747930}, {1468324,1749212}, {1511930,1598470}, {1669910,2062570}, {1798875,1870245}, {2082464,2090656}, {2236570,2429030}, {2652728,2941672}, {2723792,2874064}, {2728726,3077354}, {2739704,2928136}, {2802416,2947216}, {2803580,3716164}, {3276856,3721544}, {3606850,3892670}, {3786904,4300136}, {3805264,4006736}, {4238984,4314616}, {4246130,4488910}, {4259750,4445050}, {4482765,5120595}, {4532710,6135962}, {4604776,5162744}, {5123090,5504110}, {5147032,5843048}, {5232010,5799542}, {5357625,5684679}, {5385310,5812130}, {5459176,5495264}, {5726072,6369928}, {5730615,6088905}, {5864660,7489324}, {6329416,6371384}, {6377175,6680025}, {6955216,7418864}, {6993610,7158710}, {7275532,7471508}, {7288930,8221598}, {7489112,7674088}, {7577350,8493050}, {7677248,7684672}, {7800544,7916696}, {7850512,8052488}, {8262136,8369864}, {8619765,9627915}, {8666860,10638356}, {8754130,10893230}, {8826070,10043690}, {9071685,9498555}, {9199496,9592504}, {9206925,10791795}, {9339704,9892936}, {9363584,9437056}, {9478910,11049730}, {9491625,10950615}, {9660950,10025290}, {9773505,11791935}, {10254970,10273670}, {10533296,10949704}, {10572550,10854650}, {10596368,11199112}, {10634085,14084763}, {10992735,12070305}, {11173460,13212076}, {11252648,12101272}, {11498355,12024045}, {11545616,12247504}, {11693290,12361622}, {11905504,13337336}, {12397552,13136528}, {12707704,14236136}, {13671735,15877065}, {13813150,14310050}, {13921528,13985672}, {14311688,14718712}, {14426230,18087818}, {14443730,15882670}, {14654150,16817050}, {15002464,15334304}, {15363832,16517768}, {15938055,17308665}, {16137628,16150628}, {16871582,19325698}, {17041010,19150222}, {17257695,17578785}, {17754165,19985355}, {17844255,19895265}, {17908064,18017056}, {18056312,18166888}, {18194715,22240485}, {18655744,19154336}, {20014808,21457192}, {20022328,22823432}, {20308995,20955645}, {21448630,23030090}, {22227075,24644925}, {22249552,25325528}, {22508145,23111055}, {22608632,25775368}, {23358248,25233112}, {23389695,25132545}, {23628940,27428276}, {24472180,30395276}, {25596544,25640096}, {25966832,26529808}, {26090325,26138475}, {28118032,28128368}, {28608424,29603576}, {30724694,32174506}, {30830696,31652704}, {31536855,32148585}, {31818952,34860248}, {32205616,34352624}, {32642324,35095276}, {32685250,34538270}, {33501825,36136575}, {34256222,35997346}, {34364912,34380688}, {34765731,36939357}, {35115795,43266285}, {35361326,40117714}, {35373195,40105845}, {35390008,39259592}, {35472592,36415664}, {37363095,45663849}, {37784810,39944086}, {37848915,39202605}, {38400512,38938288}, {38637016,40678184}, {38663950,43362050}, {38783992,41654408}, {38807968,40912232}, {43096904,46715896}, {44139856,44916944}, {45263384,46137016}, {46237730,61319902}, {46271745,49125375}, {46521405,53011395}, {46555250,55880590}, {46991890,48471470}, {48639032,52967368}, {48641584,48852176}, {49215166,55349570}, {50997596,51737764}, {52695376,56208368}, {56055872,56598208}, {56512610,75866014}, {56924192,64562488}, {58580540,70507972}, {59497888,61953512}, {63560025,65003175}, {63717615,66011985}, {66595130,74824390}, {66854710,71946890}, {67729064,69439576}, {67738268,79732132}, {68891992,78437288}, {71015260,85458596}, {71241830,78057370}, {72958556,74733604}, {73032872,78469528}, {74055952,78166448}, {74386305,87354495}, {74769345,82824255}, {75171808,77237792}, {75226888,81265112}, {78088504,88110536}, {78447010,80960990}, {79324875,87133365}, {80422335,82977345}, {82633005,104177619}, {83135650,85603550}, {84521745,107908335}, {84591405,89590995}, {86158220,99188788}, {87998470,102358010}, {88144630,102814490}, {89477984,92143456}, {90437150,94372450}, {91996816,93259184}, {93837808,99899792}, {95629904,97580944}, {95791430,115187002}, {96304845,96747315}, {97041735,97945785}, {102023145,116970399}, {102719740,129063812}, {103034776,105016424}, {104887448,105064552}, {108734050,116251550}, {109410345,110132055}, {110960710,125222330}, {114944072,125269528}, {115259625,123757335}, {115447424,118458976}, {115749344,116983744}, {116654896,120115664}, {118458830,131819506}, {120812175,126671985}, {121293315,138690045}, {127924335,148532625}, {131118975,132926625}, {131483835,132692805}, {133089500,176374564}, {133178325,133471275}, {133768816,141213584}, {134312152,139057448}, {134886465,147382335}, {136549413,140207067}, {136770075,155711205}, {137424188,141993412}, {138605350,147313850}, {139009990,156322490}, {140744835,166562685}, {140815384,155709416}, {144788020,186088988}, {145040288,149364256}, {146648612,159017308}, {147366765,182028483}, {148077644,160128436}, {153015550,168392450}, {154190750,190889986}, {155578180,172610492}, {155797390,165195890}, {156226856,165181144}, {157151410,163634510}, {161088158,166706530}, {162936904,166679096}, {164733752,166212808}, {165323696,167155024}, {165742395,182622405}, {166737550,188953970}, {168930032,179904784}, {169000448,173499952}, {169335790,179029010}, {169652512,173269088}, {169884784,173843216}, {170566690,197704670}, {172271385,197261415}, {175032884,175826716}, {176632390,182618810}, {177997352,182108128}, {180038452,193486028}, {181088985,184694055}, {182702024,184713976}, {183408615,190055385}, {186753688,208059752}, {186878110,196323170}, {189406984,203592056}, {190888155,194594085}, {195857415,196214265}, {196421715,224703405}, {199432948,213484172}, {200328232,206790368}, {200879055,206393265}, {201168592,203314448}, {203055622,210627578}, {203972715,207429525}, {204134385,244869135}, {204756904,226163096}, {205843365,254264283}, {208693628,255308932}, {209027128,224355272}, {209309704,209816696}, {211319745,234587199}, {214748488,245201912}, {216392216,218772184}, {221397165,235831635}, {223878416,227342704}, {224888895,273272769}, {226540432,231465968}, {227443340,302651764}, {231111392,231923488}, {238162815,270560385}, {238238864,244730224}, {242126704,257841296}, {242182930,258410030}, {245618415,266560785}, {248658488,256201912}, {250876395,323303445}, {251302370,271244830}, {252551048,279327352}, {252940545,284847615}, {253703776,260678624}, {256755056,273568144}, {256948065,263110815}, {258904646,269448634}, {260231192,266171608}, {264764630,290441770}, {265192208,275148208}, {267217335,347397705}, {270039910,301444250}, {270208672,274655648}, {271048340,331636372}, {271629728,279947872}, {273141836,306014644}, {274638460,302514116}, {274893410,284512030}, {275304590,281534770}, {275631376,281207984}, {276339808,278431136}, {278247976,293288024}, {281499435,297034965}, {285627615,293528865}, {286000065,297390015}, {287250632,287551288}, {287793350,302793850}, {291679245,339731955}, {291974824,299001176}, {295824376,299072024}, {300120652,347620148}, {300208696,313576904}, {301685895,342005985}, {302424784,303107888}, {302770672,306676928}, {304443436,305517524}, {305178874,356714246}, {305363984,306962896}, {305911606,331160522}, {308939936,318479584}, {311414355,338659245}, {311913855,326754945}, {312090808,332345192}, {316293016,322375784}, {318323864,324492136}, {318580262,343312858}, {319682650,382593830}, {319904235,370086165}, {320829728,327818272}, {323401712,332270608}, {324644792,352731208}, {330811850,354858550}, {332448224,338290096}, {332573392,335955248}, {334438875,358687845}, {339981512,373803448}, {343175404,364682516}, {346657311,370393569}, {347263216,370414064}, {347401035,365917365}, {348782488,371171432}, {356775430,392753210}, {357197302,409205258}, {359156770,402020318}, {360027675,433850085}, {360172336,383753264}, {360759652,393667868}, {362645570,398531518}, {362700728,413408872}, {364182075,365012325}, {370032676,407256284}, {371840350,464106146}, {373305350,432893050}, {375401624,399982216}, {377141350,394237850}, {382170512,385592848}, {385465395,415773645}, {388904355,465418845}, {391548675,433398525}, {393463072,402877088}, {394800070,443597882}, {395378272,397151648}, {395939775,499717185}, {397287345,399052815}, {400250565,442792251}, {404185672,423336248}, {405370035,473836365}, {406640992,416370848}, {407641130,435691990}, {414195782,463973818}, {419640364,453610196}, {425948050,441853550}, {426191535,514780497}, {426386025,426684375}, {427448510,445018690}, {427950350,455921650}, {429035596,458447924}, {430848592,445657808}, {436386015,482909985}, {437888168,456351832}, {438362984,466417816}, {438452624,445419376}, {439232624,451335376}, {442480816,461479184}, {447761144,455118856}, {460122410,484817110}, {465605192,531830968}, {466389344,472453792}, {467406225,534612975}, {471696190,540842690}, {474179596,505757684}, {475838415,514823985}, {487169380,589230476}, {491373104,511419856}, {492275992,553544168}, {494495768,564811432}, {504555070,540539330}, {506468950,535495610}, {509379344,523679536}, {512412550,528145850}, {514439224,536022776}, {519257296,552549104}, {520218704,537213616}, {522145832,538318048}, {525254368,541358816}, {526271456,529709344}, {526552472,540314728}, {529714744,567997256}, {536637465,646745463}, {537882550,570975050}, {540759375,640415025}, {541114808,552968392}, {545134144,552877376}, {551388915,677841165}, {553978490,587641990}, {557346712,570983288}, {558173344,571181792}, {558410475,662939925}, {559334930,750516718}, {573216416,576387424}, {577884195,587323485}, {579926204,628681924}, {579980048,589141552}, {585057992,632663608}, {586188070,594986330}, {586200224,587353696}, {595858064,596654896}, {596668490,603557110}, {600418910,787621282}, {601020945,623232495}, {601235145,696285495}, {602035390,619418690}, {606235455,625482945}, {613290028,682191572}, {621354896,661063024}, {625955024,655391536}, {626323995,643272165}, {630007455,693778785}, {637756665,639580935}, {640001054,642416866}, {640866135,694532265}, {643006485,663361515}, {647314690,666518270}, {651016665,663576615}, {653078426,786829414}, {658009485,689830515}, {659084504,752700136}, {659854052,743584348}, {660792650,753402550}, {664747083,673747893}, {665113060,776681756}, {666030256,696630544}, {672672884,675728716}, {677781140,759308332}, {681310575,700743825}, {681709490,851406670}, {683490885,750610875}, {685939088,692097712}, {688679775,825955425}, {691075330,760392830}, {698002450,708157550}, {698049512,760728088}, {701168432,729739984}, {704374540,850529972}, {705023055,724885425}, {705280310,791333578}, {721522755,726368445}, {728921270,910259530}, {749380864,750555392}, {750893325,786508275}, {751953405,767949315}, {752458216,820021784}, {754484445,848771235}, {761197736,777413464}, {761511104,769560256}, {762662128,798845072}, {766292835,766512285}, {769289955,787384605}, {770805945,914053959}, {776813895,966751929}, {786882915,945492093}, {788056335,813177585}, {802162790,904824730}, {807848864,819234496}, {807964592,845947408}, {821903384,835551016}, {821921625,988676775}, {826499835,931912965}, {836535328,862396256}, {845397735,867557145}, {846862965,882865035}, {848764124,953056036}, {854687570,874694830}, {855737264,876651856}, {856305272,885518728}, {857161935,925581105}, {861314660,990788572}, {869530725,1045525275}, {870675856,895461104}, {874591550,986896450}, {877324936,890419064}, {891089368,993165032}, {894012525,991581075}, {894690615,934224585}, {902335744,903709952}, {903825416,972264184}, {905196776,1013228824}, {907960904,930631096}, {912404025,988724295}, {914746450,960133550}, {916021964,999258676}, {917168950,953023850}, {925949992,1001668568}, {930793204,999728396}, {932913124,1015026716}, {938304290,1344480478}, {948760928,951278752}, {949308932,1126001788}, {950850140,1047811252}, {954392504,1036457896}, {957871508,998051692}, {962951312,1003172848}, {965615992,1102800008}, {965674256,1019020144}, {967887488,1011081832}, {967947856,1031796176}, {968410624,1024180592}, {969473384,1043149816}, {969642056,1026197944}, {978888550,1048124570}, {989779882,1078636118}, {991838384,1025532496}, {992776995,1008990045}, {994945490,1331936326}, {996088412,1030959268}} Berechnet mit dem Mathematica-Script: In[1]:=weiter[n_] := Total[Divisors[n]] - n; In[2]:=such2[n1_, n2_] := Module[{n0, n, temp, a = {}, b, i}, For[n0 = n1, n0 <= n2, n0++, If[Mod[n0, 1000000] == 0, NotebookDelete[temp]; temp = PrintTemporary[{n0, a}]]; n = weiter[n0]; If[weiter[n] == n0 && n > n0, AppendTo[a, {n0, n}]; NotebookDelete[temp]; temp = PrintTemporary[{n0, a}]] ]; a] In[3]:=such2[1,1000000000] Das Suchskript auf https://arndt-bruenner.de/mathe/scripts/primzahlen.htm findet die gleichen Paare.