A359730 a(n) = Sum_{d|n} 2^(d-1) * d^(n/d).

1, 5, 13, 41, 81, 245, 449, 1185, 2413, 5585, 11265, 26693, 53249, 118081, 248733, 535041, 1114113, 2390885, 4980737, 10557201, 22050797, 46265345, 96468993, 201795717, 419480401, 873123841, 1812204685, 3760019521, 7784628225, 16111126325, 33285996545, 68729044993

Offset

1,2

Links

Table of n, a(n) for n=1..32.

Formula

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

Mathematica

a[n_] := DivisorSum[n, 2^(#-1) * #^(n/#) &]; Array[a, 32] (* Amiram Eldar, Aug 14 2023 *)

Prog

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

Crossrefs

Cf. A001787, A308366, A359700.

Sequence in context: A308442 A322155 A100210 * A080267 A034735 A305464

Adjacent sequences: A359727 A359728 A359729 * A359731 A359732 A359733

Keyword

nonn

Author

Seiichi Manyama, Jan 12 2023

Status

approved