OFFSET
1,2
LINKS
Seiichi Manyama, Table of n, a(n) for n = 1..1000
FORMULA
L.g.f.: -log(Product_{k>=1} (1 - k^2*x^k)^(1/k^2)) = Sum_{k>=1} a(k)*x^k/k.
a(p) = p+1 for prime p.
G.f.: Sum_{k>=1} k*x^k/(1 - k^2*x^k). - Ilya Gutkovskiy, Jul 25 2019
MATHEMATICA
a[n_] := DivisorSum[n, #^(2*n/# - 1) &]; Array[a, 37] (* 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^2)))))
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Jun 17 2019
STATUS
approved