A055895 Inverse Moebius transform of powers of 2.

1, 2, 6, 10, 22, 34, 78, 130, 278, 522, 1062, 2050, 4190, 8194, 16518, 32810, 65814, 131074, 262734, 524290, 1049654, 2097290, 4196358, 8388610, 16781662, 33554466, 67117062, 134218250, 268451990, 536870914, 1073775726, 2147483650, 4295033110, 8589936650

Offset

0,2

Comments

Row sums of A055894.

Links

T. D. Noe, Table of n, a(n) for n = 0..1000

N. J. A. Sloane, Transforms

Formula

G.f.: 1 + Sum_{k>=1} 2^k*x^k/(1-x^k). - Benoit Cloitre, Apr 21 2003

a(n) = Sum_{d divides n} 2^d. - Olivier Gérard, Jan 01 2012

a(n) = 2 * A034729(n) for n >= 1. - Joerg Arndt, Aug 14 2012

G.f.: 1 + Sum_{k>=1} 2*x^k/(1-2*x^k). - Joerg Arndt, Mar 28 2013

Example

G.f. = 1 + 2*x + 6*x^2 + 10*x^3 + 22*x^4 + 34*x^5 + 78*x^6 + 130*x^7 + ...

Mathematica

Table[Plus @@ Map[Function[d, 2^d], Divisors[n]], {n, 0, 30}] (* Olivier Gérard, Jan 01 2012 *)
a[0]=1; a[n_] := DivisorSum[n, 2^#&]; Array[a, 40, 0] (* Jean-François Alcover, Dec 01 2015 *)

Prog

(PARI) a(n)=if(n<1, 1, polcoeff(sum(k=1, n, 1/(1-2*x^k), x*O(x^n)), n))
(PARI) a(n)=if(n<1, 1, sumdiv(n, d, 2^d)); /* Joerg Arndt, Aug 14 2012 */

Crossrefs

Cf. A034729, A113705 (binary), A339916.

Cf. A055894.

Sequence in context: A371283 A182000 A167512 * A125527 A200572 A342136

Adjacent sequences: A055892 A055893 A055894 * A055896 A055897 A055898

Keyword

nonn

Author

Christian G. Bower, Jun 09 2000

Status

approved