A054598 a(0)=0; for n>0, a(n) = Sum_{d|n} d*2^(n/d).

0, 2, 8, 14, 32, 42, 104, 142, 320, 554, 1128, 2070, 4352, 8218, 16696, 32934, 66176, 131106, 263480, 524326, 1050912, 2097634, 4198488, 8388654, 16786688, 33554642, 67125352, 134219390, 268468960, 536870970, 1073811144, 2147483710, 4295099648, 8589940890

Offset: 0

Author

N. J. A. Sloane, Apr 16 2000

Keywords

• nonn

Comments

Row sums of A322200, where A322200 describes Sum_{n>=1} -log(1 - (x^n + y^n)). - Paul D. Hanna, Dec 01 2018

Crossrefs

Cf. A054599, A054600, A054601, A000016, A000031.

Cf. A322200.

Programs

Mathematica

Table[CoefficientList[Series[-Log[-QPochhammer[2, x]], {x, 0, 60}], x][[n]] (n - 1), {n, 1, 60}] (* Benedict W. J. Irwin, Jun 23 2016 *)

PARI

a(n) = sumdiv(n, d, d*2^(n/d)); \\ Michel Marcus, Jul 01 2016

Formula

L.g.f.: -log(Product_{ k>0 } (1-2*x^k)) = Sum_{ n>=0 } (a(n)/n)*x^n. - Benedict W. J. Irwin, Jun 23 2016

G.f.: Sum_{k>=1} 2^k*x^k/(1 - x^k)^2. - Ilya Gutkovskiy, Oct 24 2018