A359731 a(n) = (1/2) * Sum_{d|n} (2*d)^d.

1, 9, 109, 2057, 50001, 1493109, 52706753, 2147485705, 99179645293, 5120000050009, 292159150705665, 18260173719523445, 1240576436601868289, 91029559915023973833, 7174453500000000050109, 604462909807316734838793, 54214017802982966177103873

Offset

1,2

Links

Seiichi Manyama, Table of n, a(n) for n = 1..351

Formula

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

Mathematica

a[n_] := DivisorSum[n, (2*#)^# &] / 2; Array[a, 20] (* Amiram Eldar, Aug 14 2023 *)

Prog

(PARI) a(n) = sumdiv(n, d, (2*d)^d)/2;
(PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=1, N, 2^(k-1)*(k*x)^k/(1-x^k)))

Crossrefs

Cf. A062796, A076723, A359732.

Sequence in context: A349335 A291815 A261502 * A105974 A053912 A053894

Adjacent sequences: A359728 A359729 A359730 * A359732 A359733 A359734

Keyword

nonn,easy

Author

Seiichi Manyama, Jan 12 2023

Status

approved