A342629 a(n) = Sum_{d|n} (n/d)^(n-d).

1, 3, 10, 69, 626, 7866, 117650, 2101265, 43047451, 1000390658, 25937424602, 743069105634, 23298085122482, 793728614541474, 29192926269590300, 1152925902670135553, 48661191875666868482, 2185913413229070900339, 104127350297911241532842

Offset

1,2

Links

Seiichi Manyama, Table of n, a(n) for n = 1..387

Formula

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

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

Mathematica

a[n_] := DivisorSum[n, (n/#)^(n - #) &]; Array[a, 20] (* Amiram Eldar, Mar 17 2021 *)

Prog

(PARI) a(n) = sumdiv(n, d, (n/d)^(n-d));
(PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=1, N, k^(k-1)*x^k/(1-k^(k-1)*x^k)))
(Python)
from sympy import divisors
def A342629(n): return sum((n//d)**(n-d) for d in divisors(n, generator=True)) # Chai Wah Wu, Jun 19 2022

Crossrefs

Cf. A023887, A055225, A308668, A342628.

Sequence in context: A080526 A359701 A308814 * A232213 A143083 A002499

Adjacent sequences: A342626 A342627 A342628 * A342630 A342631 A342632

Keyword

nonn

Author

Seiichi Manyama, Mar 16 2021

Status

approved