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A054599 a(n) = Sum_{d|n} d*2^(n/d - 1). 6

%I

%S 0,1,4,7,16,21,52,71,160,277,564,1035,2176,4109,8348,16467,33088,

%T 65553,131740,262163,525456,1048817,2099244,4194327,8393344,16777321,

%U 33562676,67109695,134234480,268435485,536905572,1073741855,2147549824

%N a(n) = Sum_{d|n} d*2^(n/d - 1).

%H G. C. Greubel, <a href="/A054599/b054599.txt">Table of n, a(n) for n = 0..3300</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/q-PochhammerSymbol.html">q-Pochhammer Symbol</a>.

%F G.f.: Sum_{n>0} n*x^n/(1-2*x^n). - _Vladeta Jovovic_, Oct 27 2002

%F L.g.f.: -log(-(2;-x)_inf)/2, where (a;q)_inf is the q-Pochhammer symbol. - _Vladimir Reshetnikov_, Nov 20 2015

%F G.f.: Sum_{k>=1} 2^(k-1)*x^k/(1 - x^k)^2. - _Ilya Gutkovskiy_, Sep 10 2019

%F a(n) ~ 2^(n-1). - _Vaclav Kotesovec_, Oct 16 2019

%e G.f. = x + 4*x^2 + 7*x^3 + 16*x^4 + 21*x^5 + 52*x^6 + 71*x^7 + 160*x^8 + 277*x^9 + ...

%t {0}~Join~Table[DivisorSum[n, 2^(n/# - 1) # &], {n, 1, 20}] (* _Vladimir Reshetnikov_, Nov 20 2015 *)

%t Table[SeriesCoefficient[-Log[-QPochhammer[2, x]] n/2, {x, 0, n}], {n, 0, 20}] (* _Vladimir Reshetnikov_, Nov 20 2015 *)

%o (PARI) a(n) = if (n<1, 0, sumdiv(n, d, d*2^(n/d - 1))); \\ _Michel Marcus_, Nov 21 2015

%Y Cf. A000016, A000031, A054598, A054600, A054601.

%K nonn

%O 0,3

%A _N. J. A. Sloane_, Apr 16 2000

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Last modified August 7 17:44 EDT 2020. Contains 336278 sequences. (Running on oeis4.)