A359442 a(n) = Sum_{d|n} d^(n + 1 - d - n/d).

1, 2, 2, 4, 2, 15, 2, 74, 83, 643, 2, 12635, 2, 117715, 397188, 2359426, 2, 103572204, 2, 1260918355, 13841818644, 25937425627, 2, 5612318393211, 152587890627, 23298085126579, 1853020231898564, 2422197090649523, 2, 1032944452284531101, 2, 10376297939508166658

Offset: 1

Author

Seiichi Manyama, Jan 14 2023

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..605

Crossrefs

Cf. A294645, A342628, A342629, A342677, A359700.

Programs

Mathematica

a[n_] := DivisorSum[n, #^(n + 1 - # - n/#) &]; Array[a, 32] (* Amiram Eldar, Aug 09 2023 *)

PARI

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

PARI

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

Formula

G.f.: Sum_{k>0} x^k / (1 - (k * x)^k / k).

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