A360759 a(n) = Sum_{d|n} d^(d+n/d) * binomial(d,n/d).

1, 16, 243, 4112, 78125, 1680345, 40353607, 1073766400, 31381060338, 1000000781250, 34522712143931, 1283918489808640, 51185893014090757, 2177953338656796883, 98526125335697265625, 4722366482899710050304, 239072435685151324847153

Offset: 1

Author

Seiichi Manyama, Feb 19 2023

Keywords

• nonn

Links

• Winston de Greef, Table of n, a(n) for n = 1..383

Crossrefs

Cf. A318636, A327238, A338685, A338693, A338694.

Cf. A360712.

Programs

Mathematica

a[n_] := DivisorSum[n, #^(# + n/#) * Binomial[#, n/#] &]; Array[a, 20] (* Amiram Eldar, Aug 02 2023 *)

PARI

a(n) = sumdiv(n, d, d^(d+n/d)*binomial(d, n/d));

PARI

my(N=20, x='x+O('x^N)); Vec(sum(k=1, N, k^k*((1+k*x^k)^k-1)))

Formula

G.f.: Sum_{k>0} k^k * ( (1 + k*x^k)^k - 1 ).

If p is prime, a(p) = p^(p+2).