A367493 a(n) = Sum_{d|n} (n-d)^n.

0, 1, 8, 97, 1024, 20450, 279936, 7509953, 144295424, 4570291850, 100000000000, 4491754172274, 106993205379072, 5221973073321002, 171975117132398592, 8931527427394008833, 295147905179352825856, 20290116242888952838355, 708235345355337676357632, 51879761166564630630389778

Offset: 1

Author

Chai Wah Wu, Nov 20 2023

Keywords

• nonn

Crossrefs

Cf. A094471, A367326, A367327, A367368.

Programs

Mathematica

a[n_]:=Sum[(n-d)^n,{d,Divisors[n]}]; Array[a,20] (* Stefano Spezia, Nov 20 2023 *)

Python

from sympy import divisors
def A367493(n): return sum((n-d)**n for d in divisors(n, generator=True))

Formula

a(n) = Sum_{k=0..n} (-1)^k*binomial(n,k)*n^(n-k)*sigma_k(n).