A080267 a(n) = Sum_{d divides n} d*2^(n-n/d).

1, 5, 13, 41, 81, 257, 449, 1313, 2497, 6465, 11265, 33665, 53249, 143617, 269313, 672257, 1114113, 3159041, 4980737, 13568001, 23904257, 57675777, 96468993, 275980289, 424673281, 1090535425, 1963720705, 4823482369, 7784628225

Offset: 1

Author

Vladeta Jovovic, Feb 11 2003

Keywords

• nonn

Links

• Robert Israel, Table of n, a(n) for n = 1..3307

Crossrefs

Cf. A075900, A359112.

Programs

Maple

oo := 40; s1 := add( k*2^(k-1)*x^k/(1-2^(k-1)*x^k),k=1..oo): s2 := series(s1,x,oo-1): s3 := seriestolist(%): A080267 := n->s3[n+1];

Mathematica

a[n_] := Sum[d*2^(n-n/d), {d, Divisors[n]}]; Array[a, 29] (* Jean-François Alcover, Mar 20 2014 *)

PARI

a(n) = sumdiv(n, d, d*2^(n-n/d)); \\ Michel Marcus, Mar 20 2014

PARI

my(N=30, x='x+O('x^N)); Vec(sum(k=1, N, x^k/(1-(2*x)^k)^2)) \\ Seiichi Manyama, Dec 20 2022

Formula

G.f.: Sum_{k>=1} k*2^(k-1)*x^k/(1 - 2^(k-1)*x^k). - N. J. A. Sloane, Jun 04 2003

G.f.: Sum_{k>=1} x^k/(1 - (2 * x)^k)^2. - Seiichi Manyama, Dec 20 2022