A342675 a(n) = Sum_{d|n} d^(n-d+1).

1, 3, 4, 13, 6, 120, 8, 1161, 2197, 16148, 12, 603190, 14, 5773008, 50422464, 201359377, 18, 16590656229, 20, 269768284118, 4748723771432, 3138430473896, 24, 2972582195034162, 476837158203151, 3937376419253748, 1350852564961601560, 4066515044181860654, 30, 1036488835382356683530, 32

Offset

1,2

Links

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

Formula

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

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

Mathematica

a[n_] := DivisorSum[n, #^(n - # + 1) &]; Array[a, 30] (* Amiram Eldar, Mar 18 2021 *)

Prog

(PARI) a(n) = sumdiv(n, d, d^(n-d+1));
(PARI) my(N=40, x='x+O('x^N)); Vec(sum(k=1, N, k*x^k/(1-(k*x)^k)))

Crossrefs

Cf. A023887, A294645, A342628, A342677.

Sequence in context: A308688 A324501 A359112 * A330158 A082197 A138101

Adjacent sequences: A342672 A342673 A342674 * A342676 A342677 A342678

Keyword

nonn

Author

Seiichi Manyama, Mar 18 2021

Status

approved