A359134 a(n) = Sum_{d|n} (2*d)^(n/d - 1).

1, 3, 5, 13, 17, 55, 65, 201, 293, 779, 1025, 3365, 4097, 12303, 17781, 49681, 65537, 204547, 262145, 791549, 1095429, 3145751, 4194305, 12897625, 16787217, 50331675, 68788805, 201591509, 268435457, 815505231, 1073741825, 3223326753, 4355433957, 12884901923

Offset: 1

Author

Seiichi Manyama, Jan 13 2023

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A087909, A278741, A349970, A359733, A359796.

Programs

Mathematica

a[n_] := DivisorSum[n, (2*#)^(n/# - 1) &]; Array[a, 30] (* Amiram Eldar, Aug 14 2023 *)

PARI

a(n) = sumdiv(n, d, (2*d)^(n/d-1));

PARI

my(N=40, x='x+O('x^N)); Vec(sum(k=1, N, x^k/(1-2*k*x^k)))

Formula

G.f.: Sum_{k>0} x^k / (1 - 2 * k * x^k).

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