A347405 a(n) = Sum_{d|n} 2^(tau(d) - 1).

1, 3, 3, 7, 3, 13, 3, 15, 7, 13, 3, 49, 3, 13, 13, 31, 3, 49, 3, 49, 13, 13, 3, 185, 7, 13, 15, 49, 3, 159, 3, 63, 13, 13, 13, 341, 3, 13, 13, 185, 3, 159, 3, 49, 49, 13, 3, 713, 7, 49, 13, 49, 3, 185, 13, 185, 13, 13, 3, 2275, 3, 13, 49, 127, 13, 159, 3, 49, 13, 159, 3, 2525, 3, 13, 49, 49

Offset

1,2

Links

Seiichi Manyama, Table of n, a(n) for n = 1..10000

Formula

If p is prime, a(p^n) = 2^(n+1) - 1.

G.f.: Sum_{k>=1} 2^(tau(k) - 1) * x^k/(1 - x^k).

Mathematica

a[n_] := DivisorSum[n, 2^(DivisorSigma[0, #] - 1) &]; Array[a, 80] (* Amiram Eldar, Oct 08 2021 *)

Prog

(PARI) a(n) = sumdiv(n, d, 2^(numdiv(d)-1));
(PARI) my(N=99, x='x+O('x^N)); Vec(sum(k=1, N, 2^(numdiv(k)-1)*x^k/(1-x^k)))

Crossrefs

Cf. A000005 (tau), A000225, A347991, A347992.

Sequence in context: A119347 A323774 A062402 * A294015 A156838 A274845

Adjacent sequences: A347402 A347403 A347404 * A347406 A347407 A347408

Keyword

nonn

Author

Seiichi Manyama, Oct 08 2021

Status

approved