A376015 a(n) = Sum_{d|n} d^n * binomial(n/d,d).

1, 2, 3, 20, 5, 198, 7, 1544, 19692, 10250, 11, 2187216, 13, 344078, 143489085, 4296802320, 17, 7757846982, 19, 5497605324820, 366112362126, 230686742, 23, 4237941811999056, 298023223876953150, 5234491418, 640550188738935, 2522015815755104284

Offset: 1

Author

Seiichi Manyama, Sep 06 2024

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..724

Crossrefs

Cf. A023887, A338685.

Programs

PARI

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

PARI

my(N=30, x='x+O('x^N)); Vec(sum(k=1, N, ((k*x)^k)^k/(1-(k*x)^k)^(k+1)))

Python

from math import comb
from itertools import takewhile
from sympy import divisors
def A376015(n): return sum(d**n*comb(n//d,d) for d in takewhile(lambda d:d**2<=n,divisors(n))) # Chai Wah Wu, Sep 06 2024

Formula

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

If p is prime, a(p) = p.