A054599 a(n) = Sum_{d|n} d*2^(n/d - 1).

0, 1, 4, 7, 16, 21, 52, 71, 160, 277, 564, 1035, 2176, 4109, 8348, 16467, 33088, 65553, 131740, 262163, 525456, 1048817, 2099244, 4194327, 8393344, 16777321, 33562676, 67109695, 134234480, 268435485, 536905572, 1073741855, 2147549824

Offset

0,3

Links

G. C. Greubel, Table of n, a(n) for n = 0..3300

Eric Weisstein's World of Mathematics, q-Pochhammer Symbol.

Formula

G.f.: Sum_{n>0} n*x^n/(1-2*x^n). - Vladeta Jovovic, Oct 27 2002

L.g.f.: -log(-(2;-x)_inf)/2, where (a;q)_inf is the q-Pochhammer symbol. - Vladimir Reshetnikov, Nov 20 2015

G.f.: Sum_{k>=1} 2^(k-1)*x^k/(1 - x^k)^2. - Ilya Gutkovskiy, Sep 10 2019

a(n) ~ 2^(n-1). - Vaclav Kotesovec, Oct 16 2019

Example

G.f. = x + 4*x^2 + 7*x^3 + 16*x^4 + 21*x^5 + 52*x^6 + 71*x^7 + 160*x^8 + 277*x^9 + ...

Mathematica

{0}~Join~Table[DivisorSum[n, 2^(n/# - 1) # &], {n, 1, 20}] (* Vladimir Reshetnikov, Nov 20 2015 *)
Table[SeriesCoefficient[-Log[-QPochhammer[2, x]] n/2, {x, 0, n}], {n, 0, 20}] (* Vladimir Reshetnikov, Nov 20 2015 *)

Prog

(PARI) a(n) = if (n<1, 0, sumdiv(n, d, d*2^(n/d - 1))); \\ Michel Marcus, Nov 21 2015

Crossrefs

Cf. A000016, A000031, A054598, A054600, A054601.

Sequence in context: A299423 A067398 A325657 * A285998 A229917 A095755

Adjacent sequences: A054596 A054597 A054598 * A054600 A054601 A054602

Keyword

nonn

Author

N. J. A. Sloane, Apr 16 2000

Status

approved