# This b-file was computed by Antti Karttunen, 2019-06-03 (the first 62 terms) & Giovanni Resta, 2019-06-08 # # The first 62 terms were calculated # in GP/PARI CALCULATOR Version 2.9.4 (released) amd64 running linux (x86-64/GMP-6.1.2 kernel) 64-bit version, compiled: Dec 19 2017, gcc version 7.3.0 (Ubuntu 7.3.0-1ubuntu1), threading engine: pthread # with the following program: # # default(parisizemax,2^31); # A034448(n) = { my(f=factorint(n)); prod(k=1, #f~, 1+(f[k, 1]^f[k, 2])); }; \\ After code in A034448 # A034460(n) = (A034448(n) - n); # A048250(n) = factorback(apply(p -> p+1,factor(n)[,1])); # A325313(n) = (A048250(n) - n); # A325977(n) = ((A034460(n)+A325313(n))/2); # A162296(n) = sumdiv(n, d, d*(1-issquarefree(d))); # A325314(n) = (n - A162296(n)); # A048146(n) = (sigma(n)-A034448(n)); # A325814(n) = (n-A048146(n)); # A325978(n) = ((A325314(n)+A325814(n))/2); # A325975(n) = gcd(A325977(n), A325978(n)); # isA325981(n) = ((n%2)&&!isprime(n)&&(A325975(n)==abs(A325977(n)))); # k=0; for(n=1,oo,if(!(n%2^29),print("(n=", n,")")); if(isA325981(n), k++; print("n=",n, " -> ", factor(n)); write("b325981.txt", k, " ", n))); 1 45 2 495 3 585 4 765 5 855 6 1305 7 18837 8 21525 9 31635 10 38295 11 45315 12 50445 13 51255 14 60435 15 63495 16 68085 17 77265 18 96615 19 1403115 20 2446353 21 3411975 22 3999465 23 4091745 24 4233537 25 4287255 26 4631319 27 10813425 28 10967085 29 11490345 30 15578199 31 16143309 32 16329645 33 16633071 34 17179515 35 17311203 36 17355915 37 21159075 38 21933975 39 22579725 40 26454225 41 31102605 42 35621865 43 38555235 44 38864295 45 39327885 46 53522145 47 77960385 48 96884955 49 102876435 50 109004085 51 152063175 52 164095407 53 506676177 54 507133095 55 533995371 56 645765813 57 1072964277 58 1199924595 59 1226244075 60 1258414479 61 2009266623 62 2919199437 63 3530096925 64 3943240665 65 4036031181 66 6608604225 67 6904815687 68 7026833745 69 7433717655 70 8079575295 71 10238658345 72 13300559265 73 14817263475 74 17784748695 75 20867825115 76 20994424227 77 21432729675 78 21474083169 79 21926661939 80 27577738215 81 27716962095 82 29212838685 83 29500402239 84 29506499253 85 30406801455 86 30423677715 87 35252179245 88 37513079685 89 37848377295 90 39920042175 91 43841092113 92 46446195465 93 58324092615 94 58430453697 95 64018806579 96 67512016665 97 69405880365 98 70748883075 99 78700506435 100 83093652585 101 85595595255 102 87187150485 103 87256569285 104 90348539925 105 94316544525 106 95136104349 107 97218875385 108 99377400213 109 114480172845 110 115123814925 111 139071151035 112 146121476025 113 152947200525 114 157246096545 115 162508304175 116 166341435885 117 184731324795 118 231437606445 119 240388865415 120 251540191455 121 270151071687 122 290865415425 123 325095971025 124 337634387955 125 413616573279 126 427748427945 127 441916716969 128 442128484455 129 483243500817 130 498626311425 131 513996009795 132 516969793215 133 563305882293 134 572706528849 135 619758378603 136 620381581911 137 620416204317 138 621108652437 139 629146410885 140 635807806065 141 719753128335 142 846930625605 143 903485765175 144 933844099671 145 947422681275 146 970183044075 147 972034581525