OFFSET
1,3
LINKS
Seiichi Manyama, Table of n, a(n) for n = 1..10000
FORMULA
G.f.: Sum_{k >= 1} (1 - 1/(1 + x^k)^k).
G.f.: - Sum_{k >= 1} (-x)^k/(1 - x^k)^(k+1).
If p is prime, a(p) = (-1)^(p-1) + p.
MATHEMATICA
a[n_] := DivisorSum[n, (-1)^(# - 1) * Binomial[# + n/# - 1, #] &]; Array[a, 60] (* Amiram Eldar, Apr 24 2021 *)
PROG
(PARI) a(n) = sumdiv(n, d, (-1)^(d-1)*binomial(d+n/d-1, d));
(PARI) N=66; x='x+O('x^N); Vec(sum(k=1, N, 1-1/(1+x^k)^k))
(PARI) N=66; x='x+O('x^N); Vec(-sum(k=1, N, (-x)^k/(1-x^k)^(k+1)))
CROSSREFS
KEYWORD
sign
AUTHOR
Seiichi Manyama, Apr 23 2021
STATUS
approved