OFFSET
1,3
FORMULA
G.f.: Sum_{k>=1} k * (x/(1 + k * x^k))^k.
If p is prime, a(p) = (-1)^(p-1) + p.
MATHEMATICA
a[n_] := -DivisorSum[n, (-n/#)^# * Binomial[# + n/# - 2, # - 1] &]; Array[a, 40] (* Amiram Eldar, Apr 24 2021 *)
PROG
(PARI) a(n) = -sumdiv(n, d, (-n/d)^d*binomial(d+n/d-2, d-1));
(PARI) N=66; x='x+O('x^N); Vec(sum(k=1, N, k*(x/(1+k*x^k))^k))
CROSSREFS
KEYWORD
sign
AUTHOR
Seiichi Manyama, Apr 24 2021
STATUS
approved