A359811 a(n) = Sum_{d|n} 2^(d-1) * d^(n/d-1).

1, 3, 5, 13, 17, 53, 65, 177, 293, 625, 1025, 2541, 4097, 8769, 17109, 34561, 65537, 136013, 262145, 534481, 1054629, 2110465, 4194305, 8449325, 16787217, 33615873, 67155845, 134403521, 268435457, 537370845, 1073741825, 2148270081, 4295327397, 8591179777

Offset

1,2

Links

Table of n, a(n) for n=1..34.

Formula

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

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

a(n) ~ 2^(n-1). - Vaclav Kotesovec, Jan 14 2023

Mathematica

Table[Sum[2^(d-1) * d^(n/d - 1), {d, Divisors[n]}], {n, 1, 40}] (* Vaclav Kotesovec, Jan 14 2023 *)

Prog

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

Crossrefs

Cf. A087909, A359134, A359730, A359796.

Sequence in context: A360801 A282960 A275969 * A283063 A359134 A074854

Adjacent sequences: A359808 A359809 A359810 * A359812 A359813 A359814

Keyword

nonn,easy

Author

Seiichi Manyama, Jan 14 2023

Status

approved