A342628 a(n) = Sum_{d|n} d^(n-d).

1, 2, 2, 6, 2, 45, 2, 322, 731, 3383, 2, 132901, 2, 827641, 10297068, 33570818, 2, 2578617270, 2, 44812807567, 678610493340, 285312719189, 2, 393061010002613, 95367431640627, 302875123369471, 150094917726535604, 569939345952661545, 2, 105474306078445349841, 2

Offset

1,2

Links

Seiichi Manyama, Table of n, a(n) for n = 1..599

Formula

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

If p is prime, a(p) = 2.

Mathematica

a[n_] := DivisorSum[n, #^(n - #) &]; Array[a, 30] (* Amiram Eldar, Mar 17 2021 *)

Prog

(PARI) a(n) = sumdiv(n, d, d^(n-d));
(PARI) my(N=40, x='x+O('x^N)); Vec(sum(k=1, N, x^k/(1-(k*x)^k)))
(Python)
from sympy import divisors
def A342628(n): return sum(d**(n-d) for d in divisors(n, generator=True)) # Chai Wah Wu, Jun 19 2022

Crossrefs

Cf. A023887, A062796, A308594, A342629.

Sequence in context: A293216 A319708 A230266 * A329380 A348146 A355076

Adjacent sequences: A342625 A342626 A342627 * A342629 A342630 A342631

Keyword

nonn

Author

Seiichi Manyama, Mar 16 2021

Status

approved