A152057 Sum of the distinct prime factors of 2^n-1.

0, 0, 3, 7, 8, 31, 10, 127, 25, 80, 45, 112, 28, 8191, 173, 189, 282, 131071, 102, 524287, 91, 471, 798, 178528, 286, 2433, 10925, 262737, 320, 3425, 534, 2147483647, 65819, 599598, 174765, 123150, 266, 616318400, 699053, 129646, 61789, 164524720, 5936

Offset: 0

Author

Roger L. Bagula, Nov 22 2008

Keywords

• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 0..1206 (terms 0..500 from Robert Israel)

Crossrefs

Cf. A000225, A008472, A046800, A075708.

Row sums of A060443.

Programs

Maple

sopf:= n -> convert(numtheory:-factorset(n),`+`):
seq(sopf(2^n-1),n=0..100); # Robert Israel, Jan 14 2021

Mathematica

Table[Sum[FactorInteger[2^n - 1][[m]][[1]], {m, 1, Length[FactorInteger[2^n - 1]]}], {n, 0, 50}]

Formula

a(n) = A008472(A000225(n)). - Robert Israel, Jan 14 2021

Extensions

Edited by N. J. A. Sloane, Nov 26 2008