A348350 a(n) = Sum_{d|n} d^(sigma(d) - 1).

1, 5, 28, 4101, 3126, 362797088, 823544, 4398046515205, 282429536509, 100000000000003130, 285311670612, 137370551967459378662949775392, 302875106592254, 229585692886981495483044092, 1122274146401882171630862528

Offset

1,2

Links

Table of n, a(n) for n=1..15.

Formula

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

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

Mathematica

a[n_] := DivisorSum[n, #^(DivisorSigma[1, #] - 1) &]; Array[a, 14] (* Amiram Eldar, Oct 14 2021 *)

Prog

(PARI) a(n) = sumdiv(n, d, d^(sigma(d)-1));
(PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=1, N, k^(sigma(k)-1)*x^k/(1-x^k)))

Crossrefs

Cf. A000203, A174472, A347991, A348223, A348349.

Sequence in context: A348393 A057642 A125137 * A132550 A154587 A083020

Adjacent sequences: A348347 A348348 A348349 * A348351 A348352 A348353

Keyword

nonn

Author

Seiichi Manyama, Oct 14 2021

Status

approved