A359733 a(n) = (1/2) * Sum_{d|n} (2*d)^(n/d).

1, 4, 7, 20, 21, 88, 71, 296, 373, 1084, 1035, 5084, 4109, 16496, 20787, 67728, 65553, 286516, 262163, 1070180, 1189937, 4194568, 4194327, 17760824, 16827241, 67109228, 72150655, 269503660, 268435485, 1104603808, 1073741855, 4303389216, 4476371181

Offset

1,2

Links

Table of n, a(n) for n=1..33.

Formula

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

Mathematica

a[n_] := DivisorSum[n, (2*#)^(n/#) &] / 2; Array[a, 33] (* Amiram Eldar, Aug 14 2023 *)

Prog

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

Crossrefs

Cf. A055225, A076717.

Sequence in context: A275389 A127415 A045548 * A090879 A084404 A147065

Adjacent sequences: A359730 A359731 A359732 * A359734 A359735 A359736

Keyword

nonn,easy

Author

Seiichi Manyama, Jan 12 2023

Status

approved