OFFSET
1,2
FORMULA
G.f.: Sum_{k>=1} k * x^k/(1 - k! * x^k).
If p is prime, a(p) = 1 + p.
MATHEMATICA
a[n_] := DivisorSum[n, # * (#)!^(n/# - 1) &]; Array[a, 33] (* Amiram Eldar, Aug 30 2023 *)
PROG
(PARI) a(n) = sumdiv(n, d, d*d!^(n/d-1));
(PARI) my(N=40, x='x+O('x^N)); Vec(sum(k=1, N, k*x^k/(1-k!*x^k)))
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Aug 11 2022
STATUS
approved