160705

Ruby

Numbers n such that n^2 divides A000073(n)(18)

さらに追加した。

require 'matrix'
require 'prime'
def power(a, n, mod)
  return Matrix.I(a.row_size) if n == 0
  m = power(a, n >> 1, mod)
  m = (m * m).map{|i| i % mod}
  return m if n & 1 == 0
  (m * a).map{|i| i % mod}
end
def f(m, n, mod)
  ary0 = Array.new(m, 0)
  ary0[0] = 1
  v = Vector.elements(ary0)
  ary1 = [Array.new(m, 1)]
  (0..m - 2).each{|i|
    ary2 = Array.new(m, 0)
    ary2[i] = 1
    ary1 << ary2
  }
  a = Matrix[*ary1]
  (power(a, n, mod) * v)[m - 1]
end

# チェック用
ary0 = (1..103).to_a
p ary0.select{|i| f(3, i, i * i) == 0}

ary1 =
[1, 103, 112, 2621, 30576, 77168, 694512, 9919728, 24770928, 55638128, 57268848,
 80995824, 1300820976, 2346310512, 5251205232, 18552499056, 18579650544, 46395948144,
 75003063408, 151508024304, 151705178352, 393783442416, 445306972656, 612409425264,
 661705799664, 690597394032, 1080326291184, 2004290097264, 2390491709424, 3249633454704,
 4159129331952, 4394639588976, 5788693393392, 9835507399536, 17740453781232,
 34748830731888, 45490575587184, 48634075801584, 69464048240496, 84106792604016,
 94136324051952, 140275445362416, 140480737763184, 283774529521392, 295624141398768,
 321066327284976, 401344756381296, 589929385294704, 649742749424496, 834059959784688,
 1147042853519472, 1239374962770672, 1293488919021936, 1622497195942896,
 2865640109714928, 4047233853232752, 4412969582247408, 10842222725823216,
 11626271261016048, 11895485160559728, 14314629644266224, 17089245465971952,
 18074507814954864, 33227869932247536, 40929991755739632, 75210784146090096,
 92022858874752624, 95908917873800304, 102207830579832432, 104063341133007984,
 130106162354449008, 154633366617680496, 157532022547321968, 173428661783181168,
 262735909163805168, 387867810981526512, 414670341642905712, 468380548539526896,
 572965815899039472, 635931458878964976, 1104269974879164912, 2477084848488078192,
 2592643640045011056, 3374448626065725936, 3421999174492390128, 3525638794125894768,
 5620544535283252848, 7580469007104944496, 7897007689185289584, 8265492027549395184,
 11569572598512919536, 17411037199801640304, 20225708650600807536, 22280243705728370544,
 24433402788799381104, 30600602388716675952, 39662914773368171376, 42566585957397251568,
 44968380114682747632, 46273400234881183728, 47237823104912150256, 69417208138199581296,
 79331954180061653616, 86739456097414109808, 117883656450575009904,
 165248423718382643184, 194910637942123954032, 286655770361943541104,
 289628295674915569008, 324831883519898327664, 412648089346960796784,
 416760007129145198064, 612587983054488285936, 674698718687141466864,
 991487293596548736624, 1031262448705814528112, 1073164973178900931056,
 1191099622480301400048, 1654313608218370754928, 1684815690741866692464,
 2068297662948675880176, 2475880423595785066224, 2779844031686042276592,
 2975706480688968669552, 4332194534012637447792, 4639579921218170453616,
 4885297534960510218096, 8349385280061365899632, 10527279914585532584304,
 11674117914961365108336, 12142864536348343530096, 12528765133460591044848,
 13619804135800028410608, 14864440254272845397616, 19916982257915926273776,
 23884845720370461201648, 37882752302575312514928, 42496937231276674783728,
 42502071809085835525488, 74288639370518584987248, 79727215498205052186864,
 86670078639932457122544, 98332837230431239987824, 106133531144573215880688,
 145721822991786809874288, 162463001270456627670384, 299891298601436743773936,
 321845956423880619105648, 349873179175936630167408, 500497254754097183187696,
 594972859921905679080048, 655837027552548084258288, 811475656770754999151856,
 874328073121641364048368, 3098529388193008423980144, 9471881824653925103302512,
 21865622854722636847913328, 23466377094971687027000304, 25509893146353453213068784,
 31456345807695430829868528, 44736316034253873830686704, 193741671728874600400181616,
 26608001004934392927781006704, 119675183069386283538046118967250380133556976,
 150846183425306270568198271880911593663365616,
 3196883165332515792151825975972159404507707499888,
 35251093758476397062811685957578349411598247437424,
 38364558984374718487339298289200364704810113751664,
 156640034484488859114452199305585527064381825944944,
 230186599675331184392682948743842783670892365681904,
 390493855725072664250918616237125152488824273117424,
 423011465793699086384763981309949502911648672227312,
 1115948148131925190468155927711505377905679421284336,
 2493686679828617482075738024108623327470662938458736,
 2538209232558963478446482880450818146163592626752368,
 2985096481419036616030510716035806455208685145314544,
 3203631571040413718778235462061295746473425487450992,
 3482612536514512147817884074008728884258200392306032,
 4981913783740522854300801248163060821631867685177584,
 6528154742940086664834048087768207305075326436973552,
 747076430023390282952168060498957959080001657941326832,
 813060098555853408902181748643023329189040740739015152]
p a = ary1.select{|i| f(3, i, i * i) == 0}
a.each{|i| p [i, i.prime_division]}

出力結果
[1, 103]
[1, 103, 112, 2621, 30576, 77168, 694512, 9919728, 24770928, 55638128, 57268848, 80995824, 1300820976, 2346310512, 5251205232, 18552499056, 18579650544, 46395948144, 75003063408, 151508024304, 151705178352, 393783442416, 445306972656, 612409425264, 661705799664, 690597394032, 1080326291184, 2004290097264, 2390491709424, 3249633454704, 4159129331952, 4394639588976, 5788693393392, 9835507399536, 17740453781232, 34748830731888, 45490575587184, 48634075801584, 69464048240496, 84106792604016, 94136324051952, 140275445362416, 140480737763184, 283774529521392, 295624141398768, 321066327284976, 401344756381296, 589929385294704, 649742749424496, 834059959784688, 1147042853519472, 1239374962770672, 1293488919021936, 1622497195942896, 2865640109714928, 4047233853232752, 4412969582247408, 10842222725823216, 11626271261016048, 11895485160559728, 14314629644266224, 17089245465971952, 18074507814954864, 33227869932247536, 40929991755739632, 75210784146090096, 92022858874752624, 95908917873800304, 102207830579832432, 104063341133007984, 130106162354449008, 154633366617680496, 157532022547321968, 173428661783181168, 262735909163805168, 387867810981526512, 414670341642905712, 468380548539526896, 572965815899039472, 635931458878964976, 1104269974879164912, 2477084848488078192, 2592643640045011056, 3374448626065725936, 3421999174492390128, 3525638794125894768, 5620544535283252848, 7580469007104944496, 7897007689185289584, 8265492027549395184, 11569572598512919536, 17411037199801640304, 20225708650600807536, 22280243705728370544, 24433402788799381104, 30600602388716675952, 39662914773368171376, 42566585957397251568, 44968380114682747632, 46273400234881183728, 47237823104912150256, 69417208138199581296, 79331954180061653616, 86739456097414109808, 117883656450575009904, 165248423718382643184, 194910637942123954032, 286655770361943541104, 289628295674915569008, 324831883519898327664, 412648089346960796784, 416760007129145198064, 612587983054488285936, 674698718687141466864, 991487293596548736624, 1031262448705814528112, 1073164973178900931056, 1191099622480301400048, 1654313608218370754928, 1684815690741866692464, 2068297662948675880176, 2475880423595785066224, 2779844031686042276592, 2975706480688968669552, 4332194534012637447792, 4639579921218170453616, 4885297534960510218096, 8349385280061365899632, 10527279914585532584304, 11674117914961365108336, 12142864536348343530096, 12528765133460591044848, 13619804135800028410608, 14864440254272845397616, 19916982257915926273776, 23884845720370461201648, 37882752302575312514928, 42496937231276674783728, 42502071809085835525488, 74288639370518584987248, 79727215498205052186864, 86670078639932457122544, 98332837230431239987824, 106133531144573215880688, 145721822991786809874288, 162463001270456627670384, 299891298601436743773936, 321845956423880619105648, 349873179175936630167408, 500497254754097183187696, 594972859921905679080048, 655837027552548084258288, 811475656770754999151856, 874328073121641364048368, 3098529388193008423980144, 9471881824653925103302512, 21865622854722636847913328, 23466377094971687027000304, 25509893146353453213068784, 31456345807695430829868528, 44736316034253873830686704, 193741671728874600400181616, 26608001004934392927781006704, 119675183069386283538046118967250380133556976, 150846183425306270568198271880911593663365616, 3196883165332515792151825975972159404507707499888, 35251093758476397062811685957578349411598247437424, 38364558984374718487339298289200364704810113751664, 156640034484488859114452199305585527064381825944944, 230186599675331184392682948743842783670892365681904, 390493855725072664250918616237125152488824273117424, 423011465793699086384763981309949502911648672227312, 1115948148131925190468155927711505377905679421284336, 2493686679828617482075738024108623327470662938458736, 2538209232558963478446482880450818146163592626752368, 2985096481419036616030510716035806455208685145314544, 3203631571040413718778235462061295746473425487450992, 3482612536514512147817884074008728884258200392306032, 4981913783740522854300801248163060821631867685177584, 6528154742940086664834048087768207305075326436973552, 747076430023390282952168060498957959080001657941326832, 813060098555853408902181748643023329189040740739015152]
[1, []]
[103, [[103, 1]]]
[112, [[2, 4], [7, 1]]]
[2621, [[2621, 1]]]
[30576, [[2, 4], [3, 1], [7, 2], [13, 1]]]
[77168, [[2, 4], [7, 1], [13, 1], [53, 1]]]
[694512, [[2, 4], [3, 2], [7, 1], [13, 1], [53, 1]]]
[9919728, [[2, 4], [3, 2], [7, 1], [13, 1], [757, 1]]]
[24770928, [[2, 4], [3, 1], [7, 1], [13, 1], [53, 1], [107, 1]]]
[55638128, [[2, 4], [7, 2], [13, 1], [53, 1], [103, 1]]]
[57268848, [[2, 4], [3, 1], [7, 2], [13, 1], [1873, 1]]]
[80995824, [[2, 4], [3, 2], [7, 2], [13, 1], [883, 1]]]
[1300820976, [[2, 4], [3, 2], [7, 1], [13, 1], [53, 1], [1873, 1]]]
[2346310512, [[2, 4], [3, 2], [7, 2], [13, 1], [25579, 1]]]
[5251205232, [[2, 4], [3, 2], [7, 1], [13, 1], [53, 1], [7561, 1]]]
[18552499056, [[2, 4], [3, 2], [7, 1], [13, 1], [53, 1], [26713, 1]]]
[18579650544, [[2, 4], [3, 2], [7, 1], [13, 1], [757, 1], [1873, 1]]]
[46395948144, [[2, 4], [3, 1], [7, 1], [13, 1], [53, 1], [107, 1], [1873, 1]]]
[75003063408, [[2, 4], [3, 2], [7, 1], [13, 1], [757, 1], [7561, 1]]]
[151508024304, [[2, 4], [3, 1], [7, 2], [13, 1], [53, 1], [93493, 1]]]
[151705178352, [[2, 4], [3, 2], [7, 2], [13, 1], [883, 1], [1873, 1]]]
[393783442416, [[2, 4], [3, 2], [7, 2], [13, 1], [53, 1], [107, 1], [757, 1]]]
[445306972656, [[2, 4], [3, 1], [7, 1], [13, 1], [53, 1], [107, 1], [17977, 1]]]
[612409425264, [[2, 4], [3, 2], [7, 2], [13, 1], [883, 1], [7561, 1]]]
[661705799664, [[2, 4], [3, 1], [7, 1], [13, 1], [53, 1], [107, 1], [26713, 1]]]
[690597394032, [[2, 4], [3, 1], [7, 2], [13, 1], [883, 1], [25579, 1]]]
[1080326291184, [[2, 4], [3, 2], [7, 1], [53, 1], [757, 1], [26713, 1]]]
[2004290097264, [[2, 4], [3, 2], [7, 2], [13, 1], [53, 1], [107, 1], [3853, 1]]]
[2390491709424, [[2, 4], [3, 2], [7, 1], [13, 1], [1873, 1], [97397, 1]]]
[3249633454704, [[2, 4], [3, 2], [7, 2], [13, 1], [53, 1], [757, 1], [883, 1]]]
[4159129331952, [[2, 4], [3, 2], [7, 2], [883, 1], [667549, 1]]]
[4394639588976, [[2, 4], [3, 2], [7, 2], [13, 1], [1873, 1], [25579, 1]]]
[5788693393392, [[2, 4], [3, 1], [7, 1], [13, 1], [53, 1], [107, 1], [233689, 1]]]
[9835507399536, [[2, 4], [3, 2], [7, 1], [13, 1], [53, 1], [1873, 1], [7561, 1]]]
[17740453781232, [[2, 4], [3, 2], [7, 2], [13, 1], [7561, 1], [25579, 1]]]
[34748830731888, [[2, 4], [3, 2], [7, 1], [13, 1], [53, 1], [1873, 1], [26713, 1]]]
[45490575587184, [[2, 4], [3, 2], [7, 2], [13, 1], [53, 1], [883, 1], [10597, 1]]]
[48634075801584, [[2, 4], [3, 2], [7, 2], [13, 1], [53, 1], [107, 1], [93493, 1]]]
[69464048240496, [[2, 4], [3, 1], [7, 1], [13, 1], [53, 1], [107, 1], [2804257, 1]]]
[84106792604016, [[2, 4], [3, 2], [7, 2], [13, 1], [883, 1], [1038409, 1]]]
[94136324051952, [[2, 4], [3, 2], [7, 2], [13, 1], [53, 1], [757, 1], [25579, 1]]]
[140275445362416, [[2, 4], [3, 2], [7, 1], [13, 1], [53, 1], [7561, 1], [26713, 1]]]
[140480737763184, [[2, 4], [3, 2], [7, 1], [13, 1], [757, 1], [1873, 1], [7561, 1]]]
[283774529521392, [[2, 4], [3, 1], [7, 2], [13, 1], [53, 1], [1873, 1], [93493, 1]]]
[295624141398768, [[2, 4], [3, 1], [7, 2], [13, 1], [53, 1], [1873, 1], [97397, 1]]]
[321066327284976, [[2, 4], [3, 1], [7, 2], [13, 1], [53, 1], [103, 1], [107, 1], [17977, 1]]]
[401344756381296, [[2, 4], [3, 2], [7, 2], [13, 1], [53, 1], [883, 1], [93493, 1]]]
[589929385294704, [[2, 4], [3, 1], [7, 2], [13, 1], [53, 1], [107, 1], [883, 1], [3853, 1]]]
[649742749424496, [[2, 4], [3, 2], [7, 2], [13, 1], [757, 1], [883, 1], [10597, 1]]]
[834059959784688, [[2, 4], [3, 1], [7, 1], [13, 1], [53, 1], [107, 1], [1873, 1], [17977, 1]]]
[1147042853519472, [[2, 4], [3, 2], [7, 2], [13, 1], [883, 1], [1873, 1], [7561, 1]]]
[1239374962770672, [[2, 4], [3, 1], [7, 1], [13, 1], [53, 1], [107, 1], [1873, 1], [26713, 1]]]
[1293488919021936, [[2, 4], [3, 1], [7, 2], [13, 1], [883, 1], [1873, 1], [25579, 1]]]
[1622497195942896, [[2, 4], [3, 1], [7, 2], [13, 1], [53, 1], [107, 1], [883, 1], [10597, 1]]]
[2865640109714928, [[2, 4], [3, 2], [7, 2], [13, 1], [53, 1], [883, 1], [667549, 1]]]
[4047233853232752, [[2, 4], [3, 1], [7, 2], [13, 1], [53, 1], [26713, 1], [93493, 1]]]
[4412969582247408, [[2, 4], [3, 1], [7, 1], [13, 1], [53, 1], [107, 1], [3853, 1], [46237, 1]]]
[10842222725823216, [[2, 4], [3, 1], [7, 1], [13, 1], [53, 1], [107, 1], [1873, 1], [233689, 1]]]
[11626271261016048, [[2, 4], [3, 2], [7, 2], [13, 1], [53, 1], [25579, 1], [93493, 1]]]
[11895485160559728, [[2, 4], [3, 1], [7, 1], [13, 1], [53, 1], [107, 1], [17977, 1], [26713, 1]]]
[14314629644266224, [[2, 4], [3, 1], [7, 2], [13, 1], [53, 1], [107, 1], [883, 1], [93493, 1]]]
[17089245465971952, [[2, 4], [3, 1], [7, 2], [13, 1], [53, 1], [107, 1], [3853, 1], [25579, 1]]]
[18074507814954864, [[2, 4], [3, 2], [7, 1], [13, 1], [1873, 1], [7561, 1], [97397, 1]]]
[33227869932247536, [[2, 4], [3, 2], [7, 2], [13, 1], [1873, 1], [7561, 1], [25579, 1]]]
[40929991755739632, [[2, 4], [3, 2], [7, 2], [13, 1], [757, 1], [883, 1], [667549, 1]]]
[75210784146090096, [[2, 4], [3, 1], [7, 2], [53, 1], [883, 1], [25579, 1], [26713, 1]]]
[92022858874752624, [[2, 4], [3, 2], [7, 2], [13, 1], [53, 1], [107, 1], [757, 1], [233689, 1]]]
[95908917873800304, [[2, 4], [3, 2], [7, 1], [13, 1], [53, 1], [757, 1], [1873, 1], [97397, 1]]]
[102207830579832432, [[2, 4], [3, 1], [7, 2], [13, 1], [53, 1], [107, 1], [883, 1], [667549, 1]]]
[104063341133007984, [[2, 4], [3, 1], [7, 1], [13, 1], [53, 1], [107, 1], [17977, 1], [233689, 1]]]
[130106162354449008, [[2, 4], [3, 1], [7, 1], [13, 1], [53, 1], [107, 1], [1873, 1], [2804257, 1]]]
[154633366617680496, [[2, 4], [3, 1], [7, 1], [13, 1], [53, 1], [107, 1], [26713, 1], [233689, 1]]]
[157532022547321968, [[2, 4], [3, 2], [7, 2], [13, 1], [883, 1], [1873, 1], [1038409, 1]]]
[173428661783181168, [[2, 4], [3, 2], [7, 1], [13, 1], [53, 1], [7561, 1], [33026449, 1]]]
[262735909163805168, [[2, 4], [3, 2], [7, 1], [13, 1], [53, 1], [1873, 1], [7561, 1], [26713, 1]]]
[387867810981526512, [[2, 4], [3, 1], [7, 2], [13, 1], [53, 1], [883, 1], [10597, 1], [25579, 1]]]
[414670341642905712, [[2, 4], [3, 1], [7, 2], [13, 1], [53, 1], [107, 1], [25579, 1], [93493, 1]]]
[468380548539526896, [[2, 4], [3, 2], [7, 2], [13, 1], [53, 1], [107, 1], [3853, 1], [233689, 1]]]
[572965815899039472, [[2, 4], [3, 2], [7, 2], [13, 1], [883, 1], [10597, 1], [667549, 1]]]
[635931458878964976, [[2, 4], [3, 2], [7, 2], [13, 1], [883, 1], [7561, 1], [1038409, 1]]]
[1104269974879164912, [[2, 4], [3, 2], [7, 2], [13, 1], [53, 1], [107, 1], [757, 1], [2804257, 1]]]
[2477084848488078192, [[2, 4], [3, 2], [7, 1], [13, 1], [757, 1], [7561, 1], [33026449, 1]]]
[2592643640045011056, [[2, 4], [3, 2], [7, 2], [53, 1], [883, 1], [7561, 1], [1038409, 1]]]
[3374448626065725936, [[2, 4], [3, 2], [7, 2], [13, 1], [53, 1], [757, 1], [883, 1], [1038409, 1]]]
[3421999174492390128, [[2, 4], [3, 1], [7, 2], [13, 1], [53, 1], [883, 1], [25579, 1], [93493, 1]]]
[3525638794125894768, [[2, 4], [3, 1], [7, 1], [53, 1], [107, 1], [3853, 1], [17977, 1], [26713, 1]]]
[5620544535283252848, [[2, 4], [3, 2], [7, 2], [13, 1], [53, 1], [107, 1], [3853, 1], [2804257, 1]]]
[7580469007104944496, [[2, 4], [3, 1], [7, 2], [13, 1], [53, 1], [1873, 1], [26713, 1], [93493, 1]]]
[7897007689185289584, [[2, 4], [3, 1], [7, 2], [13, 1], [53, 1], [1873, 1], [26713, 1], [97397, 1]]]
[8265492027549395184, [[2, 4], [3, 1], [7, 1], [13, 1], [53, 1], [107, 1], [1873, 1], [3853, 1], [46237, 1]]]
[11569572598512919536, [[2, 4], [3, 2], [7, 2], [13, 1], [53, 1], [883, 1], [10597, 1], [254329, 1]]]
[17411037199801640304, [[2, 4], [3, 1], [7, 1], [13, 1], [53, 1], [107, 1], [1873, 1], [3853, 1], [97397, 1]]]
[20225708650600807536, [[2, 4], [3, 2], [7, 2], [13, 1], [883, 1], [7561, 1], [33026449, 1]]]
[22280243705728370544, [[2, 4], [3, 1], [7, 1], [13, 1], [53, 1], [107, 1], [1873, 1], [17977, 1], [26713, 1]]]
[24433402788799381104, [[2, 4], [3, 1], [7, 2], [13, 1], [53, 1], [883, 1], [25579, 1], [667549, 1]]]
[30600602388716675952, [[2, 4], [3, 1], [7, 2], [13, 1], [103, 1], [883, 1], [10597, 1], [1038409, 1]]]
[39662914773368171376, [[2, 4], [3, 2], [7, 2], [13, 1], [53, 1], [107, 1], [3853, 1], [19789009, 1]]]
[42566585957397251568, [[2, 4], [3, 2], [7, 2], [13, 1], [53, 1], [107, 1], [3853, 1], [21237737, 1]]]
[44968380114682747632, [[2, 4], [3, 1], [7, 2], [13, 1], [103, 1], [883, 1], [10597, 1], [1525969, 1]]]
[46273400234881183728, [[2, 4], [3, 2], [7, 2], [13, 1], [53, 1], [107, 1], [3853, 1], [23087177, 1]]]
[47237823104912150256, [[2, 4], [3, 2], [7, 2], [13, 1], [53, 1], [883, 1], [10597, 1], [1038409, 1]]]
[69417208138199581296, [[2, 4], [3, 2], [7, 2], [13, 1], [53, 1], [883, 1], [10597, 1], [1525969, 1]]]
[79331954180061653616, [[2, 4], [3, 1], [7, 1], [13, 1], [53, 1], [107, 1], [3853, 1], [17977, 1], [46237, 1]]]
[86739456097414109808, [[2, 4], [3, 2], [7, 2], [13, 1], [53, 1], [107, 1], [3853, 1], [43276897, 1]]]
[117883656450575009904, [[2, 4], [3, 1], [7, 1], [13, 1], [53, 1], [107, 1], [3853, 1], [26713, 1], [46237, 1]]]
[165248423718382643184, [[2, 4], [3, 2], [7, 2], [13, 1], [757, 1], [883, 1], [10597, 1], [254329, 1]]]
[194910637942123954032, [[2, 4], [3, 1], [7, 1], [13, 1], [53, 1], [107, 1], [1873, 1], [17977, 1], [233689, 1]]]
[286655770361943541104, [[2, 4], [3, 1], [7, 2], [13, 1], [53, 1], [103, 1], [883, 1], [1873, 1], [1038409, 1]]]
[289628295674915569008, [[2, 4], [3, 1], [7, 1], [13, 1], [53, 1], [107, 1], [1873, 1], [26713, 1], [233689, 1]]]
[324831883519898327664, [[2, 4], [3, 2], [7, 1], [13, 1], [53, 1], [1873, 1], [7561, 1], [33026449, 1]]]
[412648089346960796784, [[2, 4], [3, 1], [7, 2], [13, 1], [53, 1], [107, 1], [883, 1], [10597, 1], [254329, 1]]]
[416760007129145198064, [[2, 4], [3, 2], [7, 2], [13, 1], [53, 1], [883, 1], [93493, 1], [1038409, 1]]]
[612587983054488285936, [[2, 4], [3, 1], [7, 2], [13, 1], [53, 1], [107, 1], [883, 1], [3853, 1], [1038409, 1]]]
[674698718687141466864, [[2, 4], [3, 2], [7, 2], [13, 1], [757, 1], [883, 1], [10597, 1], [1038409, 1]]]
[991487293596548736624, [[2, 4], [3, 2], [7, 2], [13, 1], [757, 1], [883, 1], [10597, 1], [1525969, 1]]]
[1031262448705814528112, [[2, 4], [3, 1], [7, 1], [13, 1], [53, 1], [107, 1], [3853, 1], [46237, 1], [233689, 1]]]
[1073164973178900931056, [[2, 4], [3, 2], [7, 2], [13, 1], [883, 1], [1873, 1], [10597, 1], [667549, 1]]]
[1191099622480301400048, [[2, 4], [3, 2], [7, 2], [13, 1], [883, 1], [1873, 1], [7561, 1], [1038409, 1]]]
[1654313608218370754928, [[2, 4], [3, 1], [7, 2], [13, 1], [53, 1], [107, 1], [883, 1], [3853, 1], [2804257, 1]]]
[1684815690741866692464, [[2, 4], [3, 1], [7, 2], [13, 1], [53, 1], [107, 1], [883, 1], [10597, 1], [1038409, 1]]]
[2068297662948675880176, [[2, 4], [3, 2], [7, 2], [13, 1], [53, 1], [107, 1], [757, 1], [1873, 1], [2804257, 1]]]
[2475880423595785066224, [[2, 4], [3, 1], [7, 2], [13, 1], [53, 1], [107, 1], [883, 1], [10597, 1], [1525969, 1]]]
[2779844031686042276592, [[2, 4], [3, 1], [7, 1], [13, 1], [53, 1], [107, 1], [17977, 1], [26713, 1], [233689, 1]]]
[2975706480688968669552, [[2, 4], [3, 2], [7, 2], [13, 1], [53, 1], [883, 1], [667549, 1], [1038409, 1]]]
[4332194534012637447792, [[2, 4], [3, 2], [7, 2], [13, 1], [883, 1], [7561, 1], [10597, 1], [667549, 1]]]
[4639579921218170453616, [[2, 4], [3, 2], [7, 1], [13, 1], [757, 1], [1873, 1], [7561, 1], [33026449, 1]]]
[4885297534960510218096, [[2, 4], [3, 1], [7, 2], [13, 1], [883, 1], [10597, 1], [25579, 1], [667549, 1]]]
[8349385280061365899632, [[2, 4], [3, 2], [7, 2], [13, 1], [53, 1], [107, 1], [757, 1], [7561, 1], [2804257, 1]]]
[10527279914585532584304, [[2, 4], [3, 2], [7, 2], [13, 1], [53, 1], [107, 1], [1873, 1], [3853, 1], [2804257, 1]]]
[11674117914961365108336, [[2, 4], [3, 1], [7, 2], [13, 1], [53, 1], [107, 1], [883, 1], [3853, 1], [19789009, 1]]]
[12142864536348343530096, [[2, 4], [3, 2], [7, 2], [13, 1], [883, 1], [10597, 1], [21193, 1], [667549, 1]]]
[12528765133460591044848, [[2, 4], [3, 1], [7, 2], [13, 1], [53, 1], [107, 1], [883, 1], [3853, 1], [21237737, 1]]]
[13619804135800028410608, [[2, 4], [3, 1], [7, 2], [13, 1], [53, 1], [107, 1], [883, 1], [3853, 1], [23087177, 1]]]
[14864440254272845397616, [[2, 4], [3, 1], [7, 2], [13, 1], [53, 1], [107, 1], [883, 1], [93493, 1], [1038409, 1]]]
[19916982257915926273776, [[2, 4], [3, 1], [7, 2], [53, 1], [883, 1], [10597, 1], [25579, 1], [667549, 1]]]
[23884845720370461201648, [[2, 4], [3, 1], [7, 2], [13, 1], [53, 1], [107, 1], [883, 1], [233689, 1], [667549, 1]]]
[37882752302575312514928, [[2, 4], [3, 2], [7, 2], [13, 1], [883, 1], [1873, 1], [7561, 1], [33026449, 1]]]
[42496937231276674783728, [[2, 4], [3, 2], [7, 2], [13, 1], [53, 1], [107, 1], [3853, 1], [7561, 1], [2804257, 1]]]
[42502071809085835525488, [[2, 4], [3, 2], [7, 2], [13, 1], [757, 1], [883, 1], [667549, 1], [1038409, 1]]]
[74288639370518584987248, [[2, 4], [3, 2], [7, 2], [13, 1], [53, 1], [107, 1], [1873, 1], [3853, 1], [19789009, 1]]]
[79727215498205052186864, [[2, 4], [3, 2], [7, 2], [13, 1], [53, 1], [107, 1], [1873, 1], [3853, 1], [21237737, 1]]]
[86670078639932457122544, [[2, 4], [3, 2], [7, 2], [13, 1], [53, 1], [107, 1], [1873, 1], [3853, 1], [23087177, 1]]]
[98332837230431239987824, [[2, 4], [3, 2], [7, 2], [13, 1], [53, 1], [107, 1], [757, 1], [7561, 1], [33026449, 1]]]
[106133531144573215880688, [[2, 4], [3, 1], [7, 2], [13, 1], [53, 1], [107, 1], [883, 1], [667549, 1], [1038409, 1]]]
[145721822991786809874288, [[2, 4], [3, 2], [7, 2], [13, 1], [883, 1], [10597, 1], [254329, 1], [667549, 1]]]
[162463001270456627670384, [[2, 4], [3, 2], [7, 2], [13, 1], [53, 1], [107, 1], [1873, 1], [3853, 1], [43276897, 1]]]
[299891298601436743773936, [[2, 4], [3, 2], [7, 2], [13, 1], [53, 1], [107, 1], [3853, 1], [7561, 1], [19789009, 1]]]
[321845956423880619105648, [[2, 4], [3, 2], [7, 2], [13, 1], [53, 1], [107, 1], [3853, 1], [7561, 1], [21237737, 1]]]
[349873179175936630167408, [[2, 4], [3, 2], [7, 2], [13, 1], [53, 1], [107, 1], [3853, 1], [7561, 1], [23087177, 1]]]
[500497254754097183187696, [[2, 4], [3, 2], [7, 2], [13, 1], [53, 1], [107, 1], [3853, 1], [7561, 1], [33026449, 1]]]
[594972859921905679080048, [[2, 4], [3, 2], [7, 2], [13, 1], [883, 1], [10597, 1], [667549, 1], [1038409, 1]]]
[655837027552548084258288, [[2, 4], [3, 2], [7, 2], [13, 1], [53, 1], [107, 1], [3853, 1], [7561, 1], [43276897, 1]]]
[811475656770754999151856, [[2, 4], [3, 2], [7, 2], [13, 1], [53, 1], [757, 1], [883, 1], [7561, 1], [33026449, 1]]]
[874328073121641364048368, [[2, 4], [3, 2], [7, 2], [13, 1], [883, 1], [10597, 1], [667549, 1], [1525969, 1]]]
[3098529388193008423980144, [[2, 4], [3, 1], [7, 2], [13, 1], [53, 1], [107, 1], [883, 1], [1873, 1], [3853, 1], [2804257, 1]]]
[9471881824653925103302512, [[2, 4], [3, 2], [7, 2], [13, 1], [883, 1], [10597, 1], [667549, 1], [16531321, 1]]]
[21865622854722636847913328, [[2, 4], [3, 1], [7, 2], [13, 1], [53, 1], [107, 1], [883, 1], [1873, 1], [3853, 1], [19789009, 1]]]
[23466377094971687027000304, [[2, 4], [3, 1], [7, 2], [13, 1], [53, 1], [107, 1], [883, 1], [1873, 1], [3853, 1], [21237737, 1]]]
[25509893146353453213068784, [[2, 4], [3, 1], [7, 2], [13, 1], [53, 1], [107, 1], [883, 1], [1873, 1], [3853, 1], [23087177, 1]]]
[31456345807695430829868528, [[2, 4], [3, 1], [7, 2], [53, 1], [107, 1], [883, 1], [3853, 1], [667549, 1], [1038409, 1]]]
[44736316034253873830686704, [[2, 4], [3, 1], [7, 2], [13, 1], [53, 1], [107, 1], [883, 1], [1873, 1], [233689, 1], [667549, 1]]]
[193741671728874600400181616, [[2, 4], [3, 2], [7, 2], [883, 1], [7561, 1], [10597, 1], [254329, 1], [1525969, 1]]]
[26608001004934392927781006704, [[2, 4], [3, 2], [7, 2], [883, 1], [10597, 1], [254329, 1], [1038409, 1], [1525969, 1]]]
[119675183069386283538046118967250380133556976, [[2, 4], [3, 2], [7, 2], [13, 1], [53, 1], [107, 1], [883, 1], [1873, 1], [3853, 1], [7561, 1], [10597, 1], [17977, 1], [21193, 1], [25579, 1], [46237, 1]]]
[150846183425306270568198271880911593663365616, [[2, 4], [3, 2], [7, 2], [13, 1], [53, 1], [107, 1], [883, 1], [1873, 1], [3853, 1], [7561, 1], [10597, 1], [17977, 1], [25579, 1], [26713, 1], [46237, 1]]]
[3196883165332515792151825975972159404507707499888, [[2, 4], [3, 2], [7, 2], [13, 1], [53, 1], [107, 1], [883, 1], [1873, 1], [3853, 1], [7561, 1], [10597, 1], [17977, 1], [21193, 1], [25579, 1], [26713, 1], [46237, 1]]]
[35251093758476397062811685957578349411598247437424, [[2, 4], [3, 2], [7, 2], [13, 1], [53, 1], [107, 1], [883, 1], [1873, 1], [3853, 1], [7561, 1], [10597, 1], [17977, 1], [25579, 1], [26713, 1], [46237, 1], [233689, 1]]]
[38364558984374718487339298289200364704810113751664, [[2, 4], [3, 2], [7, 2], [13, 1], [53, 1], [107, 1], [883, 1], [1873, 1], [3853, 1], [7561, 1], [10597, 1], [17977, 1], [25579, 1], [26713, 1], [46237, 1], [254329, 1]]]
[156640034484488859114452199305585527064381825944944, [[2, 4], [3, 2], [7, 2], [13, 1], [53, 1], [107, 1], [883, 1], [1873, 1], [3853, 1], [7561, 1], [10597, 1], [17977, 1], [25579, 1], [26713, 1], [46237, 1], [1038409, 1]]]
[230186599675331184392682948743842783670892365681904, [[2, 4], [3, 2], [7, 2], [13, 1], [53, 1], [107, 1], [883, 1], [1873, 1], [3853, 1], [7561, 1], [10597, 1], [17977, 1], [25579, 1], [26713, 1], [46237, 1], [1525969, 1]]]
[390493855725072664250918616237125152488824273117424, [[2, 4], [3, 2], [7, 2], [13, 1], [53, 1], [107, 1], [883, 1], [1873, 1], [3853, 1], [7561, 1], [10597, 1], [17977, 1], [25579, 1], [26713, 1], [46237, 1], [2588689, 1]]]
[423011465793699086384763981309949502911648672227312, [[2, 4], [3, 2], [7, 2], [13, 1], [53, 1], [107, 1], [883, 1], [1873, 1], [3853, 1], [7561, 1], [10597, 1], [17977, 1], [25579, 1], [26713, 1], [46237, 1], [2804257, 1]]]
[1115948148131925190468155927711505377905679421284336, [[2, 4], [3, 2], [7, 2], [13, 1], [53, 1], [107, 1], [883, 1], [1873, 1], [3853, 1], [7561, 1], [10597, 1], [17977, 1], [25579, 1], [26713, 1], [46237, 1], [7397921, 1]]]
[2493686679828617482075738024108623327470662938458736, [[2, 4], [3, 2], [7, 2], [13, 1], [53, 1], [107, 1], [883, 1], [1873, 1], [3853, 1], [7561, 1], [10597, 1], [17977, 1], [25579, 1], [26713, 1], [46237, 1], [16531321, 1]]]
[2538209232558963478446482880450818146163592626752368, [[2, 4], [3, 2], [7, 2], [13, 1], [53, 1], [107, 1], [883, 1], [1873, 1], [3853, 1], [7561, 1], [10597, 1], [17977, 1], [25579, 1], [26713, 1], [46237, 1], [16826473, 1]]]
[2985096481419036616030510716035806455208685145314544, [[2, 4], [3, 2], [7, 2], [13, 1], [53, 1], [107, 1], [883, 1], [1873, 1], [3853, 1], [7561, 1], [10597, 1], [17977, 1], [25579, 1], [26713, 1], [46237, 1], [19789009, 1]]]
[3203631571040413718778235462061295746473425487450992, [[2, 4], [3, 2], [7, 2], [13, 1], [53, 1], [107, 1], [883, 1], [1873, 1], [3853, 1], [7561, 1], [10597, 1], [17977, 1], [25579, 1], [26713, 1], [46237, 1], [21237737, 1]]]
[3482612536514512147817884074008728884258200392306032, [[2, 4], [3, 2], [7, 2], [13, 1], [53, 1], [107, 1], [883, 1], [1873, 1], [3853, 1], [7561, 1], [10597, 1], [17977, 1], [25579, 1], [26713, 1], [46237, 1], [23087177, 1]]]
[4981913783740522854300801248163060821631867685177584, [[2, 4], [3, 2], [7, 2], [13, 1], [53, 1], [107, 1], [883, 1], [1873, 1], [3853, 1], [7561, 1], [10597, 1], [17977, 1], [25579, 1], [26713, 1], [46237, 1], [33026449, 1]]]
[6528154742940086664834048087768207305075326436973552, [[2, 4], [3, 2], [7, 2], [13, 1], [53, 1], [107, 1], [883, 1], [1873, 1], [3853, 1], [7561, 1], [10597, 1], [17977, 1], [25579, 1], [26713, 1], [46237, 1], [43276897, 1]]]
[747076430023390282952168060498957959080001657941326832, [[2, 4], [3, 2], [7, 2], [13, 1], [53, 1], [107, 1], [883, 1], [1873, 1], [3853, 1], [7561, 1], [10597, 1], [17977, 1], [21193, 1], [25579, 1], [26713, 1], [46237, 1], [233689, 1]]]
[813060098555853408902181748643023329189040740739015152, [[2, 4], [3, 2], [7, 2], [13, 1], [53, 1], [107, 1], [883, 1], [1873, 1], [3853, 1], [7561, 1], [10597, 1], [17977, 1], [21193, 1], [25579, 1], [26713, 1], [46237, 1], [254329, 1]]]