OFFSET
0,3
COMMENTS
Euler transform of A000593.
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..10000 (terms 0..1000 from Vaclav Kotesovec)
FORMULA
a(n) ~ exp((3*Pi)^(2/3) * Zeta(3)^(1/3) * n^(2/3) / 2^(4/3) + 1/24) * Zeta(3)^(13/72) / (sqrt(A) * 2^(23/36) * 3^(49/72) * Pi^(13/72) * n^(49/72)), where A is the Glaisher-Kinkelin constant A074962.
G.f.: exp(Sum_{k>=1} sigma_2(k)*x^k/(k*(1 + x^k))). - Ilya Gutkovskiy, Oct 26 2018
MATHEMATICA
nmax = 40; CoefficientList[Series[Exp[Sum[Sum[DivisorSum[k, -(-1)^# k / # &] * x^(j*k) / j, {k, 1, Floor[nmax/j] + 1}], {j, 1, nmax}]], {x, 0, nmax}], x] (* Vaclav Kotesovec, Mar 31 2018 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Mar 26 2018
STATUS
approved