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A055895 Inverse Moebius transform of powers of 2. 7
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 (list; graph; refs; listen; history; text; internal format)
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( 2^d, d divides n) - 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. A055894.

Sequence in context: A055745 A182000 A167512 * A125527 A200572 A049750

Adjacent sequences:  A055892 A055893 A055894 * A055896 A055897 A055898

KEYWORD

nonn

AUTHOR

Christian G. Bower, Jun 09 2000

STATUS

approved

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Last modified July 22 21:32 EDT 2019. Contains 325227 sequences. (Running on oeis4.)