OFFSET
1,2
FORMULA
a(n) = Sum_{d|n} d^(n/d) * binomial(d+n/d-1,d).
If p is prime, a(p) = 2 * p.
MATHEMATICA
a[n_] := DivisorSum[n, #^(n/#) * Binomial[# + n/# - 1, #] &]; Array[a, 40] (* Amiram Eldar, Jul 31 2023 *)
PROG
(PARI) my(N=50, x='x+O('x^N)); Vec(sum(k=1, N, k*x^k/(1-k*x^k)^(k+1)))
(PARI) a(n) = sumdiv(n, d, d^(n/d)*binomial(d+n/d-1, d));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Feb 22 2023
STATUS
approved