A354863 a(n) = n! * Sum_{d|n} (n/d) / d!.

1, 5, 19, 121, 601, 5641, 35281, 406561, 3447361, 45420481, 439084801, 7565564161, 80951270401, 1525654690561, 20737536019201, 421943967244801, 6046686277632001, 150482493928166401, 2311256907767808001, 61410502863943833601, 1132546296081328128001

Offset

1,2

Links

Table of n, a(n) for n=1..21.

Formula

E.g.f.: Sum_{k>0} k * (exp(x^k) - 1).

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

Mathematica

a[n_] := n! * DivisorSum[n, (n/#) / #! &]; Array[a, 21] (* Amiram Eldar, Aug 30 2023 *)

Prog

(PARI) a(n) = n!*sumdiv(n, d, n/d/d!);
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(sum(k=1, N, k*(exp(x^k)-1))))
(Python)
from math import factorial
from sympy import divisors
def A354863(n):
    f = factorial(n)
    return sum(f*n//d//factorial(d) for d in divisors(n, generator=True)) # Chai Wah Wu, Jun 09 2022

Crossrefs

Cf. A057625, A354843, A354862.

Sequence in context: A339079 A357361 A209111 * A328060 A366340 A297389

Adjacent sequences: A354860 A354861 A354862 * A354864 A354865 A354866

Keyword

nonn

Author

Seiichi Manyama, Jun 09 2022

Status

approved