OFFSET
1,2
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
FORMULA
G.f.: Sum_{k >= 1} sigma(k)^3 * x^k/(1 - x^k).
If p is prime, a(p) = 1 + (p+1)^3.
Sum_{k=1..n} a(k) ~ c * n^4, where c = (Pi^10*zeta(3)/194400) * Product_{p prime} (1 + 2/p^2 + 2/p^3 + 1/p^5) = 1.6422194986... . - Amiram Eldar, Nov 20 2022
MATHEMATICA
a[n_] := DivisorSum[n, DivisorSigma[1, #]^3 &]; Array[a, 41] (* Amiram Eldar, May 08 2021 *)
PROG
(PARI) a(n) = sumdiv(n, d, sigma(d)^3);
(PARI) my(N=66, x='x+O('x^N)); Vec(sum(k=1, N, sigma(k)^3*x^k/(1-x^k)))
CROSSREFS
KEYWORD
nonn,mult
AUTHOR
Seiichi Manyama, May 08 2021
STATUS
approved