A343573 a(n) = Sum_{d|n} d^d * binomial(d+n/d-2, d-1).

1, 5, 28, 265, 3126, 46750, 823544, 16778257, 387420652, 10000015646, 285311670612, 8916100731047, 302875106592254, 11112006831322846, 437893890380906656, 18446744073843774497, 827240261886336764178, 39346408075300025340205

Offset: 1

Author

Seiichi Manyama, Apr 20 2021

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..386

Crossrefs

Cf. A023887, A157019, A157020, A324158, A324159, A338661, A339481, A339482, A339712, A343567, A343574.

Programs

Mathematica

a[n_] := DivisorSum[n, #^#*Binomial[# + n/# - 2, # - 1] &]; Array[a, 20] (* Amiram Eldar, Apr 20 2021 *)

PARI

a(n) = sumdiv(n, d, d^d*binomial(d+n/d-2, d-1));

PARI

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

Formula

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

If p is prime, a(p) = 1 + p^p.