OFFSET
1,2
FORMULA
G.f.: Sum_{k >= 1} sigma(k)^2 * x^k/(1 - x^k)^2.
From Vaclav Kotesovec, May 08 2021: (Start)
Dirichlet g.f.: zeta(s) * zeta(s-1)^3 * zeta(s-2) / zeta(2*s-2).
Sum_{k=1..n} a(k) ~ 5 * Pi^2 * zeta(3) * n^3 / 36. (End)
MATHEMATICA
a[n_] := n * DivisorSum[n, DivisorSigma[1, #]^2/# &]; Array[a, 51] (* Amiram Eldar, May 08 2021 *)
PROG
(PARI) a(n) = n*sumdiv(n, d, sigma(d)^2/d);
(PARI) my(N=66, x='x+O('x^N)); Vec(sum(k=1, N, sigma(k)^2*x^k/(1-x^k)^2))
(PARI) for(n=1, 100, print1(direuler(p=2, n, (1 - p^2*X^2) / ((1 - X) * (1 - p*X)^3 * (1 - p^2*X)))[n], ", ")) \\ Vaclav Kotesovec, May 08 2021
CROSSREFS
KEYWORD
nonn,mult
AUTHOR
Seiichi Manyama, May 08 2021
STATUS
approved