# This b-file was computed by Antti Karttunen, 2019-02-16 # 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); # A000265(n) = (n/2^valuation(n, 2)); # A324054(n) = { my(p=2,mp=p*p,m=1); while(n, if(!(n%2), p=nextprime(1+p); mp = p*p, if(3==(n%4),mp *= p,m *= (mp-1)/(p-1))); n>>=1); (m); }; # A324108(n) = { my(f=factor(n)); prod(i=1, #f~, A324054((f[i,1]^f[i,2])-1)); }; # isA324111(n) = ((1!=omega(n))&&(1!=omega(A000265(n)))&&(A324054(n-1)==A324108(n))); # k=0; n=0; while(k<10001, n++; if(isA324111(n), k++; write("b324111.txt", k, " ", n))); 1 1 2 87 3 174 4 348 5 696 6 1392 7 2091 8 2784 9 4182 10 5568 11 8364 12 11136 13 16683 14 16728 15 22272 16 33215 17 33366 18 33456 19 44544 20 66430 21 66732 22 66912 23 89088 24 132860 25 133464 26 133824 27 178176 28 265720 29 266928 30 267179 31 267648 32 356352 33 531440 34 533856 35 534358 36 535296 37 712704 38 1062880 39 1066877 40 1067712 41 1068716 42 1070592 43 1319235 44 1425408 45 2125760 46 2133754 47 2135424 48 2137432 49 2141184 50 2638470 51 2850816 52 4228521 53 4251520 54 4267508 55 4270848 56 4274864 57 4282368 58 4330579 59 5276940 60 5701632 61 8457042 62 8503040 63 8535016 64 8541696 65 8549728 66 8564736 67 8661158 68 8668351 69 9769751 70 10553880 71 11403264 72 16914084 73 17006080 74 17070032 75 17083392 76 17099456 77 17129472 78 17322316 79 17336702 80 19539502 81 21107760 82 22806528 83 33828168 84 34012160 85 34140064 86 34166784 87 34198912 88 34258944 89 34644632 90 34662043 91 34673404 92 35924003 93 39079004 94 42215520 95 45613056 96 50892875 97 67656336 98 68024320 99 68239949 100 68280128 101 68333568 102 68397824 103 68517888 104 69289264 105 69324086 106 69346808 107 71848006 108 78158008 109 83920375 110 84431040 111 91226112 112 101785750 113 135312672 114 136048640 115 136479898 116 136560256 117 136667136 118 136795648 119 137035776 120 138578528 121 138648172 122 138693616 123 143201615 124 143696012 125 151730823 126 156316016 127 167840750 128 168862080 129 182452224 130 203571500 131 270625344 132 272097280 133 272959796 134 273120512 135 273334272 136 273591296 137 274071552 138 277157056 139 277296344 140 277387232 141 286403230 142 287392024 143 303461646 144 311513495 145 312632032 146 335681500 147 337724160 148 364904448 149 407143000 150 419564887 151 537386921 152 538253299 153 539511051 154 541250688 155 544194560 156 545919592 157 546241024 158 546668544 159 547182592 160 548143104 161 554314112 162 554592688 163 554774464 164 572806460 165 574784048 166 605140375 167 606923292 168 623026990 169 625264064 170 671363000 171 675448320 172 729808896 173 814286000