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%I #51 Dec 23 2020 06:06:59
%S 1,2,6,10,22,34,78,130,278,522,1062,2050,4190,8194,16518,32810,65814,
%T 131074,262734,524290,1049654,2097290,4196358,8388610,16781662,
%U 33554466,67117062,134218250,268451990,536870914,1073775726,2147483650,4295033110,8589936650
%N Inverse Moebius transform of powers of 2.
%C Row sums of A055894.
%H T. D. Noe, <a href="/A055895/b055895.txt">Table of n, a(n) for n = 0..1000</a>
%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%F G.f.: 1 + Sum_{k>=1} 2^k*x^k/(1-x^k). - _Benoit Cloitre_, Apr 21 2003
%F a(n) = Sum_{d divides n} 2^d. - _Olivier Gérard_, Jan 01 2012
%F a(n) = 2 * A034729(n) for n >= 1. - _Joerg Arndt_, Aug 14 2012
%F G.f.: 1 + Sum_{k>=1} 2*x^k/(1-2*x^k). - _Joerg Arndt_, Mar 28 2013
%e G.f. = 1 + 2*x + 6*x^2 + 10*x^3 + 22*x^4 + 34*x^5 + 78*x^6 + 130*x^7 + ...
%t Table[Plus @@ Map[Function[d, 2^d], Divisors[n]], {n, 0, 30}] (* _Olivier Gérard_, Jan 01 2012 *)
%t a[0]=1; a[n_] := DivisorSum[n, 2^#&]; Array[a, 40, 0] (* _Jean-François Alcover_, Dec 01 2015 *)
%o (PARI) a(n)=if(n<1,1,polcoeff(sum(k=1,n,1/(1-2*x^k),x*O(x^n)),n))
%o (PARI) a(n)=if(n<1,1,sumdiv(n,d,2^d)); /* _Joerg Arndt_, Aug 14 2012 */
%Y Cf. A034729, A113705 (binary), A339916.
%Y Cf. A055894.
%K nonn
%O 0,2
%A _Christian G. Bower_, Jun 09 2000
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