A348349 a(n) = Sum_{d|n} d^(tau(d) - 1).

1, 3, 4, 19, 6, 222, 8, 531, 85, 1008, 12, 249070, 14, 2754, 3384, 66067, 18, 1889871, 20, 3201024, 9272, 10662, 24, 4586721006, 631, 17592, 19768, 17213138, 30, 21870004602, 32, 33620499, 35952, 39324, 42888, 2821112046175, 38, 54894, 59336, 163843201536

Offset

1,2

Links

Table of n, a(n) for n=1..40.

Formula

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

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

Mathematica

a[n_] := DivisorSum[n, #^(DivisorSigma[0, #] - 1) &]; Array[a, 40] (* Amiram Eldar, Oct 14 2021 *)

Prog

(PARI) a(n) = sumdiv(n, d, d^(numdiv(d)-1));
(PARI) my(N=66, x='x+O('x^N)); Vec(sum(k=1, N, k^(numdiv(k)-1)*x^k/(1-x^k)))

Crossrefs

Cf. A000005 (tau), A174937, A347405, A347992, A348350.

Sequence in context: A263968 A020344 A344459 * A248590 A143150 A100340

Adjacent sequences: A348346 A348347 A348348 * A348350 A348351 A348352

Keyword

nonn

Author

Seiichi Manyama, Oct 14 2021

Status

approved