OFFSET
1,2
FORMULA
a(n) = Sum_{d|n} 2^(n-d) * d^d * binomial(d,n/d-1).
If p is an odd prime, a(p) = p^p.
MATHEMATICA
a[n_] := DivisorSum[n, 2^(n-#) * #^# * Binomial[#, n/# - 1] &]; Array[a, 20] (* Amiram Eldar, Aug 02 2023 *)
PROG
(PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=1, N, (k*x*(1+(2*x)^k))^k))
(PARI) a(n) = sumdiv(n, d, 2^(n-d)*d^d*binomial(d, n/d-1));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Feb 19 2023
STATUS
approved