A359863 - OEIS

A359863

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

1, 4, 6, 24, 10, 156, 14, 528, 747, 1620, 22, 15000, 26, 12572, 60780, 98336, 34, 397908, 38, 1484840, 1500324, 495660, 46, 18514992, 9765675, 2768948, 28697868, 85098552, 58, 375843660, 62, 570425408, 471565380, 75759684, 2626093820, 7623165384, 74, 378536012

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OFFSET

1,2

LINKS

Seiichi Manyama, Table of n, a(n) for n = 1..5000

FORMULA

a(n) = [x^n] Sum_{k>0} k * (n * x / k)^k / (1 - k * x^k).

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

MATHEMATICA

a[n_] := DivisorSum[n, #^(n/#) * (n/#)^# &]; Array[a, 40] (* Amiram Eldar, Aug 09 2023 *)

PROG

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