A259564 Numbers n such that the sum of the prime factors (including repeats) of prime(n)-1 and prime(n+1)-1 are the same.
5, 7, 11, 30, 133, 160, 415, 527, 883, 1257, 2025, 2771, 2775, 6650, 6932, 13793, 19091, 30695, 32341, 33722, 36372, 37944, 40532, 42141, 47230, 60986, 77956, 82165, 90564, 111414, 113106, 136036, 147573, 148357, 158279, 169137, 169604, 171549, 174540, 187679
Offset: 1
Keywords
Examples
The prime factors of prime(30)-1 are 2,2,2,2,7 and the prime factors of prime(31)-1 are 2,3,3,7. The sum of entries in each of these lists is 15.
Programs
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Mathematica
SequencePosition[Table[Total[Flatten[Table[#[[1]],#[[2]]]&/@ FactorInteger[ p-1]]],{p,Prime[Range[200000]]}],{x_,x_}][[All,1]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Oct 12 2020 *) -
PARI
spff(n) = {my(f=factor(n)); sum(k=1, #f~, f[k,1]*f[k,2]);} lista(nn) = {forprime(p=2, nn, if (spff(p-1)==spff(nextprime(p+1)-1), print1(primepi(p), ", ")););} \\ Michel Marcus, Jun 30 2015
Extensions
More terms from Alois P. Heinz, Jun 30 2015
Name edited by Zak Seidov, Jul 02 2015
Comments