A174439 Partial sums of A001523.

1, 2, 4, 8, 16, 31, 58, 105, 184, 314, 523, 853, 1365, 2149, 3332, 5097, 7701, 11505, 17009, 24907, 36147, 52027, 74304, 105352, 148355, 207575, 288673, 399157, 548926, 750996, 1022400, 1385374, 1868813, 2510181, 3357862, 4474187, 5939186

Offset: 0

Author

Jonathan Vos Post, Mar 19 2010

Keywords

• easy
• nonn

Comments

The subsequence of primes begins: 2, 31, 523, 853, 24907, 52027, 1868813, ...

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A001523, A054250, A059618, A059623, A001522, A001524, A000569, A100505, A100506.

Programs

Mathematica

nmax = 41; A001523 = CoefficientList[Series[1 + Sum[(-1)^(k + 1)*x^(k*(k + 1)/2), {k, 1, nmax}] / QPochhammer[x]^2, {x, 0, nmax}], x]; s = 0; Table[s = s + A001523[[k]], {k, 1, nmax}] (* Vaclav Kotesovec, Dec 13 2015 *)

Formula

a(n) = Sum_{i=0..n} A001523(i).

a(n) ~ exp(2*Pi*sqrt(n/3))/(8*Pi*3^(1/4)*n^(3/4)). - Vaclav Kotesovec, Dec 13 2015