A359882 a(n) = Sum_{d|n} d^n * (n/d)^d.

1, 6, 30, 324, 3130, 53070, 823550, 17829896, 387951939, 10312525610, 285311670622, 9056807631948, 302875106592266, 11198819379685518, 437901307945957140, 18518802767263301648, 827240261886336764194, 39423330565860716459946

Offset: 1

Author

Seiichi Manyama, Jan 16 2023

Keywords

• nonn

Crossrefs

Cf. A066108, A308594, A359103.

Programs

Mathematica

a[n_] := DivisorSum[n, #^n * (n/#)^# &]; Array[a, 20] (* Amiram Eldar, Aug 09 2023 *)

PARI

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

Formula

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

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