A358660 a(n) = Sum_{d|n} d * (n/d)^(n-d).

1, 4, 12, 76, 630, 7968, 117656, 2105416, 43048917, 1000781420, 25937424612, 743130116112, 23298085122494, 793742455829456, 29192926758107760, 1152930300766980112, 48661191875666868498, 2185915267189632382650, 104127350297911241532860

Offset: 1

Author

Seiichi Manyama, Dec 17 2022

Keywords

• nonn

Links

• Sidney Cadot, Table of n, a(n) for n = 1..100

Crossrefs

Cf. A090879, A342629, A356539, A359112.

Programs

Mathematica

a[n_] := Total[Map[#*(n/#)^(n - #) &, Divisors[n]]];
Table[a[n],{n,1,100}]
a[n_] := DivisorSum[n, (n/#)^(n-#)*# &]; Array[a, 19] (* Amiram Eldar, Aug 27 2023 *)

PARI

a(n) = sumdiv(n, d, 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)^2))

Formula

G.f.: Sum_{k>=1} k^(k-1) * x^k/(1 - k^(k-1) * x^k)^2.

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