OFFSET
1,2
FORMULA
G.f.: Sum_{k>0} (1/k) * (1/(1 - k * x^k)^k - 1).
If p is prime, a(p) = 1 + p.
MATHEMATICA
a[n_] := DivisorSum[n, (n/#)^(#-1) * Binomial[# + n/# - 1, #] &]; Array[a, 50] (* Amiram Eldar, Jul 31 2023 *)
PROG
(PARI) a(n) = sumdiv(n, d, (n/d)^(d-1)*binomial(d+n/d-1, d));
(PARI) my(N=50, x='x+O('x^N)); Vec(sum(k=1, N, (1/(1-k*x^k)^k-1)/k))
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Feb 26 2023
STATUS
approved