OFFSET
1,3
COMMENTS
Convolution of sigma with sigma_2.
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 1..10000
FORMULA
G.f.: ( Sum_{k>=1} k * x^k/(1 - x^k) ) * ( Sum_{k>=1} k^2 * x^k/(1 - x^k) ).
Sum_{k=1..n} a(k) ~ Pi^2 * zeta(3) * n^5 / 360. - Vaclav Kotesovec, Sep 19 2024
MATHEMATICA
Table[Sum[DivisorSigma[1, k]*DivisorSigma[2, n-k], {k, 1, n-1}], {n, 1, 50}] (* Vaclav Kotesovec, Sep 19 2024 *)
PROG
(PARI) a(n) = sum(k=1, n-1, sigma(k, 1)*sigma(n-k, 2));
(PARI) my(N=50, x='x+O('x^N)); concat(0, Vec(sum(k=1, N, k*x^k/(1-x^k))*sum(k=1, N, k^2*x^k/(1-x^k))))
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Seiichi Manyama, Jul 26 2024
STATUS
approved