OFFSET
1,2
FORMULA
a(n) = Sum_{d|n} 2^(n-d) * binomial(d+n/d-2,d-1).
If p is prime, a(p) = 1 + 2^(p-1).
MATHEMATICA
a[n_] := DivisorSum[n, 2^(n-#) * Binomial[# + n/# - 2, # - 1] &]; Array[a, 30] (* Amiram Eldar, Aug 02 2023 *)
PROG
(PARI) my(N=40, x='x+O('x^N)); Vec(sum(k=1, N, (x/(1-(2*x)^k))^k))
(PARI) a(n) = sumdiv(n, d, 2^(n-d)*binomial(d+n/d-2, d-1));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Feb 21 2023
STATUS
approved