OFFSET
1,2
COMMENTS
If p is prime, a(p) = p * Sum_{d|p} sigma_d(d) / d = p * (1 + (1^p + p^p)/p) = 1 + p + p^p.
LINKS
Seiichi Manyama, Table of n, a(n) for n = 1..386
FORMULA
G.f.: Sum_{k>=1} sigma_k(k) * x^k/(1 - x^k)^2. - Seiichi Manyama, Dec 16 2022
EXAMPLE
a(4) = 4 * Sum_{d|4} sigma_d(d) / d = 4 * ((1^1)/1 + (1^2 + 2^2)/2 + (1^4 + 2^4 + 4^4)/4) = 287.
MATHEMATICA
Table[n*Sum[DivisorSigma[k, k] (1 - Ceiling[n/k] + Floor[n/k])/k, {k, n}], {n, 20}]
PROG
(PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=1, N, sigma(k, k)*x^k/(1-x^k)^2)) \\ Seiichi Manyama, Dec 16 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, May 28 2021
STATUS
approved