180621

Ruby


(1 - b*x)^(1/A003557(b))

b が1728以下で、A003557(b) > 1 となる場合について
出力してみた。

require 'prime'

def f(n)
  return 1 if n < 2
  (1..n).inject(:*)
end

def A003557(n)
  s = 1
  n.prime_division.each{|i| s *= i[0] ** (i[1] - 1)}
  s
end

def A(a, k, n)
  [1] + (1..n).map{|i| (k / a) ** i * (0..i - 1).inject(1){|s, j| s * (a * j - 1)} / f(i)}
end

n = 6
(1..1728).each{|i|
  a = A003557(i)
  p [i, a, A(a, i, n)] if a > 1
}

出力結果
[4, 2, [1, -2, -2, -4, -10, -28, -84]]
[8, 4, [1, -2, -6, -28, -154, -924, -5852]]
[9, 3, [1, -3, -9, -45, -270, -1782, -12474]]
[12, 2, [1, -6, -18, -108, -810, -6804, -61236]]
[16, 8, [1, -2, -14, -140, -1610, -19964, -259532]]
[18, 3, [1, -6, -36, -360, -4320, -57024, -798336]]
[20, 2, [1, -10, -50, -500, -6250, -87500, -1312500]]
[24, 4, [1, -6, -54, -756, -12474, -224532, -4266108]]
[25, 5, [1, -5, -50, -750, -13125, -249375, -4987500]]
[27, 9, [1, -3, -36, -612, -11934, -250614, -5513508]]
[28, 2, [1, -14, -98, -1372, -24010, -470596, -9882516]]
[32, 16, [1, -2, -30, -620, -14570, -367164, -9668652]]
[36, 6, [1, -6, -90, -1980, -50490, -1393524, -40412196]]
[40, 4, [1, -10, -150, -3500, -96250, -2887500, -91437500]]
[44, 2, [1, -22, -242, -5324, -146410, -4509428, -148811124]]
[45, 3, [1, -15, -225, -5625, -168750, -5568750, -194906250]]
[48, 8, [1, -6, -126, -3780, -130410, -4851252, -189198828]]
[49, 7, [1, -7, -147, -4459, -156065, -5899257, -234003861]]
[50, 5, [1, -10, -200, -6000, -210000, -7980000, -319200000]]
[52, 2, [1, -26, -338, -8788, -285610, -10396204, -405451956]]
[54, 9, [1, -6, -144, -4896, -190944, -8019648, -352864512]]
[56, 4, [1, -14, -294, -9604, -369754, -15529668, -688481948]]
[60, 2, [1, -30, -450, -13500, -506250, -21262500, -956812500]]
[63, 3, [1, -21, -441, -15435, -648270, -29950074, -1467553626]]
[64, 32, [1, -2, -62, -2604, -123690, -6283452, -333022956]]
[68, 2, [1, -34, -578, -19652, -835210, -39755996, -2027555796]]
[72, 12, [1, -6, -198, -9108, -478170, -26968788, -1591158492]]
[75, 5, [1, -15, -450, -20250, -1063125, -60598125, -3635887500]]
[76, 2, [1, -38, -722, -27436, -1303210, -69330772, -3951854004]]
[80, 8, [1, -10, -350, -17500, -1006250, -62387500, -4055187500]]
[81, 27, [1, -3, -117, -6201, -372060, -23886252, -1600378884]]
[84, 2, [1, -42, -882, -37044, -1944810, -114354828, -7204354164]]
[88, 4, [1, -22, -726, -37268, -2254714, -148811124, -10367174972]]
[90, 3, [1, -30, -900, -45000, -2700000, -178200000, -12474000000]]
[92, 2, [1, -46, -1058, -48668, -2798410, -180217604, -12435014676]]
[96, 16, [1, -6, -270, -16740, -1180170, -89220852, -7048447308]]
[98, 7, [1, -14, -588, -35672, -2497040, -188776224, -14976247104]]
[99, 3, [1, -33, -1089, -59895, -3953070, -286992882, -22098451914]]
[100, 10, [1, -10, -450, -28500, -2066250, -161167500, -13162012500]]
[104, 4, [1, -26, -1014, -61516, -4398394, -343074732, -28246486268]]
[108, 18, [1, -6, -306, -21420, -1702890, -145086228, -12912674292]]
[112, 8, [1, -14, -686, -48020, -3865610, -335534948, -30533680268]]
[116, 2, [1, -58, -1682, -97556, -7072810, -574312172, -49965158964]]
[117, 3, [1, -39, -1521, -98865, -7711470, -661644126, -60209615466]]
[120, 4, [1, -30, -1350, -94500, -7796250, -701662500, -66657937500]]
[121, 11, [1, -11, -605, -46585, -4099480, -387810808, -38393269992]]
[124, 2, [1, -62, -1922, -119164, -9235210, -801616228, -74550309204]]
[125, 25, [1, -5, -300, -24500, -2266250, -224358750, -23183737500]]
[126, 3, [1, -42, -1764, -123480, -10372320, -958402368, -93923432064]]
[128, 64, [1, -2, -126, -10668, -1018794, -103916988, -11049839724]]
[132, 2, [1, -66, -2178, -143748, -11859210, -1095791004, -108483309396]]
[135, 9, [1, -15, -900, -76500, -7458750, -783168750, -86148562500]]
[136, 4, [1, -34, -1734, -137564, -12862234, -1311947868, -141253053788]]
[140, 2, [1, -70, -2450, -171500, -15006250, -1470612500, -154414312500]]
[144, 24, [1, -6, -414, -38916, -4144554, -472479156, -56225019564]]
[147, 7, [1, -21, -1323, -120393, -12641265, -1433519451, -170588814669]]
[148, 2, [1, -74, -2738, -202612, -18741610, -1941630796, -215521018356]]
[150, 5, [1, -30, -1800, -162000, -17010000, -1939140000, -232696800000]]
[152, 4, [1, -38, -2166, -192052, -20069434, -2287915476, -275312495612]]
[153, 3, [1, -51, -2601, -221085, -22550670, -2530185174, -301092035706]]
[156, 2, [1, -78, -3042, -237276, -23134410, -2526277572, -295574475924]]
[160, 16, [1, -10, -750, -77500, -9106250, -1147387500, -151072687500]]
[162, 27, [1, -6, -468, -49608, -5952960, -764360064, -102424248576]]
[164, 2, [1, -82, -3362, -275684, -28257610, -3243973628, -399008756244]]
[168, 4, [1, -42, -2646, -259308, -29950074, -3773709324, -501903340092]]
[169, 13, [1, -13, -1014, -109850, -13566475, -1798914585, -249449489120]]
[171, 3, [1, -57, -3249, -308655, -35186670, -4412408418, -586850319594]]
[172, 2, [1, -86, -3698, -318028, -34188010, -4116236404, -530994496116]]
[175, 5, [1, -35, -2450, -257250, -31513125, -4191245625, -586774387500]]
[176, 8, [1, -22, -1694, -186340, -23572010, -3215222164, -459776769452]]
[180, 6, [1, -30, -2250, -247500, -31556250, -4354762500, -631440562500]]
[184, 4, [1, -46, -3174, -340676, -43095514, -5947180932, -866306022428]]
[188, 2, [1, -94, -4418, -415292, -48796810, -6421660196, -905454087636]]
[189, 9, [1, -21, -1764, -209916, -28653534, -4212069498, -648658702692]]
[192, 32, [1, -6, -558, -70308, -10018890, -1526878836, -242773734924]]
[196, 14, [1, -14, -1274, -160524, -23035194, -3547419876, -571134600036]]
[198, 3, [1, -66, -4356, -479160, -63249120, -9183772224, -1414300922496]]
[200, 20, [1, -10, -950, -123500, -18216250, -2878167500, -474897637500]]
[204, 2, [1, -102, -5202, -530604, -67652010, -9660707028, -1478088175284]]
[207, 3, [1, -69, -4761, -547515, -75557070, -11469563226, -1846599679386]]
[208, 8, [1, -26, -2366, -307580, -45983210, -7412493452, -1252711393388]]
[212, 2, [1, -106, -5618, -595508, -78904810, -11709473804, -1861806334836]]
[216, 36, [1, -6, -630, -89460, -14358330, -2463889428, -441036207612]]
[220, 2, [1, -110, -6050, -665500, -91506250, -14091962500, -2325173812500]]
[224, 16, [1, -14, -1470, -212660, -34982570, -6170925348, -1137507239148]]
[225, 15, [1, -15, -1575, -228375, -37681875, -6669691875, -1233892996875]]
[228, 2, [1, -114, -6498, -740772, -105560010, -16847377596, -2880901568916]]
[232, 4, [1, -58, -5046, -682892, -108921274, -18952301676, -3480906074492]]
[234, 3, [1, -78, -6084, -790920, -123383520, -21172612032, -3853415389824]]
[236, 2, [1, -118, -6962, -821516, -121173610, -20017880372, -3543164825844]]
[240, 8, [1, -30, -3150, -472500, -81506250, -15160162500, -2956231687500]]
[242, 11, [1, -22, -2420, -372680, -65591680, -12409945856, -2457169279488]]
[243, 81, [1, -3, -360, -57960, -10519740, -2038725612, -411822573624]]
[244, 2, [1, -122, -7442, -907924, -138458410, -23648696428, -4327711446324]]
[245, 7, [1, -35, -3675, -557375, -97540625, -18435178125, -3656310328125]]
[248, 4, [1, -62, -5766, -834148, -142222234, -26453335524, -5193671541212]]
[250, 25, [1, -10, -1200, -196000, -36260000, -7179480000, -1483759200000]]
[252, 6, [1, -42, -4410, -679140, -121226490, -23420957868, -4754454447204]]
[256, 128, [1, -2, -254, -43180, -8268970, -1690177468, -360007800684]]
[260, 2, [1, -130, -8450, -1098500, -178506250, -32488137500, -6335186812500]]
[261, 3, [1, -87, -7569, -1097505, -190965870, -36550867518, -7419826106154]]
[264, 4, [1, -66, -6534, -1006236, -182631834, -36161103132, -7557670554588]]
[268, 2, [1, -134, -8978, -1203052, -201511210, -37803502996, -7598504102196]]
[270, 9, [1, -30, -3600, -612000, -119340000, -25061400000, -5513508000000]]
[272, 8, [1, -34, -4046, -687820, -134468810, -28346025148, -6264471557708]]
[275, 5, [1, -55, -6050, -998250, -192163125, -40162093125, -8835660487500]]
[276, 2, [1, -138, -9522, -1314036, -226671210, -43792877772, -9065125698804]]
[279, 3, [1, -93, -8649, -1340595, -249350670, -51017147082, -11070720916794]]
[280, 4, [1, -70, -7350, -1200500, -231096250, -48530212500, -10757530437500]]
[284, 2, [1, -142, -10082, -1431644, -254116810, -50518421828, -10760423849364]]
[288, 48, [1, -6, -846, -160740, -34478730, -7902524916, -1888703454924]]
[289, 17, [1, -17, -2312, -432344, -91873100, -20928692180, -4981028738840]]
[292, 2, [1, -146, -10658, -1556068, -283982410, -58046004604, -12712075008276]]
[294, 7, [1, -42, -5292, -963144, -202260240, -45872622432, -10917684138816]]
[296, 4, [1, -74, -8214, -1418284, -288620794, -64073816268, -15014630945468]]
[297, 9, [1, -33, -4356, -814572, -174725694, -40361635314, -9767515745988]]
[300, 10, [1, -30, -4050, -769500, -167366250, -39163702500, -9595107112500]]
[304, 8, [1, -38, -5054, -960260, -209816810, -49432840436, -12209911587692]]
[306, 3, [1, -102, -10404, -1768680, -360810720, -80965925568, -19269890285184]]
[308, 2, [1, -154, -11858, -1826132, -351530410, -75789956396, -17507479927476]]
[312, 4, [1, -78, -9126, -1660932, -356269914, -83367159876, -20591688489372]]
[315, 3, [1, -105, -11025, -1929375, -405168750, -93593981250, -22930525406250]]
[316, 2, [1, -158, -12482, -1972156, -389500810, -86157579172, -20419346263764]]
[320, 32, [1, -10, -1550, -325500, -77306250, -19635787500, -5203483687500]]
[324, 54, [1, -6, -954, -204156, -49303674, -12720347892, -3421773582948]]
[325, 5, [1, -65, -8450, -1647750, -374863125, -92591191875, -24073709887500]]
[328, 4, [1, -82, -10086, -1929788, -435167194, -107051129724, -27797610018332]]
[332, 2, [1, -166, -13778, -2287148, -474583210, -110293138004, -27462991362996]]
[333, 3, [1, -111, -12321, -2279385, -506023470, -123570931374, -32004871225866]]
[336, 8, [1, -42, -6174, -1296540, -313114410, -81534992364, -22259052915372]]
[338, 13, [1, -26, -4056, -878800, -217063600, -57565266720, -15964767303680]]
[340, 2, [1, -170, -14450, -2456500, -522006250, -124237487500, -31680559312500]]
[342, 3, [1, -114, -12996, -2469240, -562986720, -141197069376, -37558420454016]]
[343, 49, [1, -7, -1176, -266168, -68005924, -18565617252, -5285012377736]]
[344, 4, [1, -86, -11094, -2226196, -526495354, -135835801332, -36992616562748]]
[348, 2, [1, -174, -15138, -2634012, -572897610, -139557857796, -36424600884756]]
[350, 5, [1, -70, -9800, -2058000, -504210000, -134119860000, -37553560800000]]
[351, 9, [1, -39, -6084, -1344564, -340846974, -93051223902, -26612650035972]]
[352, 16, [1, -22, -3630, -825220, -213319370, -59132129364, -17128606805772]]
[356, 2, [1, -178, -15842, -2819876, -627422410, -156353664572, -41746428440724]]
[360, 12, [1, -30, -4950, -1138500, -298856250, -84277462500, -24861851437500]]
[361, 19, [1, -19, -3249, -761349, -202518834, -57717867690, -17180685282390]]
[363, 11, [1, -33, -5445, -1257795, -332057880, -94238026344, -27988693824168]]
[364, 2, [1, -182, -16562, -3014284, -685749610, -174729000628, -47701017171444]]
[368, 8, [1, -46, -7406, -1703380, -450544010, -128495151652, -38420050343948]]
[369, 3, [1, -123, -15129, -3101445, -762955470, -206455750182, -59252800302234]]
[372, 2, [1, -186, -17298, -3217428, -748052010, -194792743404, -54347175409716]]
[375, 25, [1, -15, -2700, -661500, -183566250, -54519176250, -16900944637500]]
[376, 4, [1, -94, -13254, -2907044, -751470874, -211914786468, -63079968105308]]
[378, 9, [1, -42, -7056, -1679328, -458456544, -134786223936, -41514156972288]]
[380, 2, [1, -190, -18050, -3429500, -814506250, -216658662500, -61747718812500]]
[384, 64, [1, -6, -1134, -288036, -82522314, -25251828084, -8055333158796]]
[387, 3, [1, -129, -16641, -3577815, -923076270, -261969045426, -78852682673226]]
[388, 2, [1, -194, -18818, -3650692, -885292810, -240445527196, -69969648414036]]
[392, 28, [1, -14, -2646, -679140, -197290170, -61317784836, -19887401548476]]
[396, 6, [1, -66, -10890, -2635380, -739224090, -224428433724, -71592670357956]]
[400, 40, [1, -10, -1950, -513500, -152766250, -48579667500, -16112256387500]]
[404, 2, [1, -202, -20402, -4121204, -1040604010, -294282814028, -89167692650484]]
[405, 27, [1, -15, -2925, -775125, -232537500, -74644537500, -25005920062500]]
[408, 4, [1, -102, -15606, -3714228, -1041840954, -318803331924, -102973476211452]]
[412, 2, [1, -206, -21218, -4370908, -1125508810, -324596740804, -100300392908436]]
[414, 3, [1, -138, -19044, -4380120, -1208913120, -367026023232, -118182379480704]]
[416, 16, [1, -26, -5070, -1362140, -416133770, -136325423052, -46668736491468]]
[420, 2, [1, -210, -22050, -4630500, -1215506250, -357358837500, -112568033812500]]
[423, 3, [1, -141, -19881, -4672035, -1317513870, -408692802474, -134459932013946]]
[424, 4, [1, -106, -16854, -4168556, -1215134074, -386412635532, -129705841326908]]
[425, 5, [1, -85, -14450, -3684750, -1096213125, -354076839375, -120386125387500]]
[428, 2, [1, -214, -22898, -4900172, -1310796010, -392714484596, -126061349555316]]
[432, 72, [1, -6, -1278, -365508, -117876330, -40596608052, -14574182290668]]
[436, 2, [1, -218, -23762, -5180116, -1411581610, -430814707372, -140876409310644]]
[440, 4, [1, -110, -18150, -4658500, -1409196250, -465034762500, -161987108937500]]
[441, 21, [1, -21, -4410, -1265670, -411975585, -143614688931, -52275746770884]]
[444, 2, [1, -222, -24642, -5470524, -1518070410, -471816283428, -157114822381524]]
[448, 32, [1, -14, -3038, -893172, -296979690, -105605977764, -39179817750444]]
[450, 15, [1, -30, -6300, -1827000, -602910000, -213430140000, -78969151800000]]
[452, 2, [1, -226, -25538, -5771588, -1630473610, -515881850204, -174883947219156]]
[456, 4, [1, -114, -19494, -5185404, -1625624154, -555963460668, -200702809301148]]
[459, 9, [1, -51, -10404, -3006756, -996739614, -355836042198, -133082679782052]]
[460, 2, [1, -230, -26450, -6083500, -1749006250, -563180012500, -194297104312500]]
[464, 8, [1, -58, -11774, -3414460, -1138722410, -409484578636, -154375686145772]]
[468, 6, [1, -78, -15210, -4350060, -1442044890, -517405706532, -195061951362564]]
[472, 4, [1, -118, -20886, -5750612, -1866073594, -660590052276, -246840482867132]]
[475, 5, [1, -95, -18050, -5144250, -1710463125, -617477188125, -234641331487500]]
[476, 2, [1, -238, -28322, -6740636, -2005339210, -668179024772, -238539911843604]]
[477, 3, [1, -159, -25281, -6699465, -2130429870, -745224368526, -276478240723146]]
[480, 16, [1, -30, -6750, -2092500, -737606250, -278815162500, -110131989187500]]
[484, 22, [1, -22, -5082, -1602524, -572902330, -219307011924, -87649702432292]]
[486, 81, [1, -6, -1440, -463680, -168315840, -65239219584, -26356644711936]]
[488, 4, [1, -122, -22326, -6355468, -2132259514, -780406982124, -301497230760572]]
[490, 7, [1, -70, -14700, -4459000, -1560650000, -589925700000, -234003861000000]]
[492, 2, [1, -246, -30258, -7443468, -2288866410, -788285591604, -290877383301876]]
[495, 3, [1, -165, -27225, -7486875, -2470668750, -896852756250, -345288311156250]]
[496, 8, [1, -62, -13454, -4170740, -1486868810, -571552370564, -230335605337292]]
[500, 50, [1, -10, -2450, -808500, -301166250, -119864167500, -49743629512500]]
[504, 12, [1, -42, -9702, -3124044, -1148086170, -453264419916, -187198205425308]]
[507, 13, [1, -39, -9126, -2965950, -1098884475, -437136244155, -181848677568480]]
[508, 2, [1, -254, -32258, -8193532, -2601446410, -925074343396, -352453324833876]]
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