OFFSET
1,2
FORMULA
G.f.: Sum_{k>0} 2^(k-1) * x^k / (1 - k * x^k).
If p is prime, a(p) = 1 + 2^(p-1).
a(n) ~ 2^(n-1). - Vaclav Kotesovec, Jan 14 2023
MATHEMATICA
Table[Sum[2^(d-1) * d^(n/d - 1), {d, Divisors[n]}], {n, 1, 40}] (* Vaclav Kotesovec, Jan 14 2023 *)
PROG
(PARI) a(n) = sumdiv(n, d, 2^(d-1)*d^(n/d-1));
(PARI) my(N=40, x='x+O('x^N)); Vec(sum(k=1, N, 2^(k-1)*x^k/(1-k*x^k)))
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Seiichi Manyama, Jan 14 2023
STATUS
approved