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
Keywords
Examples
G.f. = 1 + 2*x + 6*x^2 + 10*x^3 + 22*x^4 + 34*x^5 + 78*x^6 + 130*x^7 + ...
Links
- T. D. Noe, Table of n, a(n) for n = 0..1000
- N. J. A. Sloane, Transforms
Programs
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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 *) -
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 */
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
Comments