OFFSET
1,2
LINKS
Robert Israel, Table of n, a(n) for n = 1..3143
FORMULA
L.g.f.: -log(Product_{k>=1} (1 - k^2*x^k)^(1/k^3)) = Sum_{k>=1} a(k)*x^k/k.
a(p) = 2 for prime p.
G.f.: Sum_{k>=1} x^k/(1 - k^2*x^k). - Ilya Gutkovskiy, Jul 25 2019
MAPLE
N:=100: # for a(1)..a(N)
g:= add(x^k/(1-k^2*x^k), k=1..N):
S:= series(g, x, N+1):
seq(coeff(S, x, j), j=1..N); # Robert Israel, Apr 05 2020
MATHEMATICA
a[n_] := DivisorSum[n, #^(2*(n/# - 1)) &]; Array[a, 39] (* Amiram Eldar, May 09 2021 *)
PROG
(PARI) {a(n) = sumdiv(n, d, d^(2*(n/d-1)))}
(PARI) N=66; x='x+O('x^N); Vec(x*deriv(-log(prod(k=1, N, (1-k^2*x^k)^(1/k^3)))))
CROSSREFS
KEYWORD
nonn,look
AUTHOR
Seiichi Manyama, Jun 17 2019
STATUS
approved