A301543 Expansion of Product_{k>=1} 1/(1 - x^k)^(sigma_5(k)).

1, 1, 34, 278, 1896, 13074, 92442, 607200, 3866890, 24062327, 146637082, 873517399, 5101981085, 29274370913, 165261721720, 918756928198, 5035250026792, 27229238821726, 145412875008092, 767414597651951, 4004930689994100, 20679955170511834, 105711772783426512

Offset: 0

Author

Vaclav Kotesovec, Mar 23 2018

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..2331

Crossrefs

Product_{k>=1} 1/(1 - x^k)^sigma_m(k): A006171 (m=0), A061256 (m=1), A275585 (m=2), A288391 (m=3), A301542 (m=4), this sequence (m=5), A301544 (m=6), A301545 (m=7), A301546 (m=8), A301547 (m=9).

Cf. A001160, A301549.

Programs

Mathematica

nmax = 30; CoefficientList[Series[Product[1/(1-x^k)^DivisorSigma[5, k], {k, 1, nmax}], {x, 0, nmax}], x]

Formula

a(n) ~ exp((7*Pi)^(6/7) * (Zeta(7)/3)^(1/7) * n^(6/7) / (3*2^(3/7)) - Zeta'(-5)/2) * (Zeta(7)/(3*Pi))^(251/3528) / (2^(251/1176) * 7^(2015/3528) * n^(2015/3528)).

G.f.: exp(Sum_{k>=1} sigma_6(k)*x^k/(k*(1 - x^k))). - Ilya Gutkovskiy, Oct 26 2018