A342677 a(n) = Sum_{d|n} (n/d)^(n-d+1).

1, 5, 28, 265, 3126, 46916, 823544, 16793633, 387422677, 10001953190, 285311670612, 8916464313700, 302875106592254, 11112103714568680, 437893891601739648, 18446779258148749825, 827240261886336764178, 39346424755299348744797, 1978419655660313589123980

Offset: 1

Author

Seiichi Manyama, Mar 18 2021

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..386

Crossrefs

Cf. A294645, A342629, A342675.

Programs

Mathematica

a[n_] := DivisorSum[n, (n/#)^(n - # + 1) &]; Array[a, 20] (* Amiram Eldar, Mar 18 2021 *)

PARI

a(n) = sumdiv(n, d, (n/d)^(n-d+1));

PARI

my(N=20, x='x+O('x^N)); Vec(sum(k=1, N, (k*x)^k/(1-k^(k-1)*x^k)))

Formula

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

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