OFFSET
1,2
FORMULA
G.f.: Sum_{k>=1} (k * x/(1 + (k * x)^k))^k.
If p is prime, a(p) = (-1)^(p-1) + p^p.
MATHEMATICA
a[n_] := DivisorSum[n, (-1)^(# - 1) * (n/#)^n * Binomial[# + n/# - 2, # - 1] &]; Array[a, 20] (* Amiram Eldar, Apr 24 2021 *)
PROG
(PARI) a(n) = sumdiv(n, d, (-1)^(d-1)*(n/d)^n*binomial(d+n/d-2, d-1));
(PARI) N=20; x='x+O('x^N); Vec(sum(k=1, N, (k*x/(1+(k*x)^k))^k))
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Apr 24 2021
STATUS
approved