OFFSET
1,2
FORMULA
a(n) = Sum_{d|n} 2^(n/d-1) * binomial(d+n/d-1,d).
If p is prime, a(p) = 1 + p * 2^(p-1).
MATHEMATICA
a[n_] := DivisorSum[n, 2^(n/# - 1) * Binomial[# + n/# - 1, #] &]; Array[a, 30] (* Amiram Eldar, Jul 31 2023 *)
PROG
(PARI) my(N=40, x='x+O('x^N)); Vec(sum(k=1, N, x^k/(1-2*x^k)^(k+1)))
(PARI) a(n) = sumdiv(n, d, 2^(n/d-1)*binomial(d+n/d-1, d));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Feb 21 2023
STATUS
approved