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%I #18 Dec 01 2018 11:02:01
%S 0,2,8,14,32,42,104,142,320,554,1128,2070,4352,8218,16696,32934,66176,
%T 131106,263480,524326,1050912,2097634,4198488,8388654,16786688,
%U 33554642,67125352,134219390,268468960,536870970,1073811144,2147483710,4295099648,8589940890
%N a(0)=0; for n>0, a(n) = Sum_{d|n} d*2^(n/d).
%C Row sums of A322200, where A322200 describes Sum_{n>=1} -log(1 - (x^n + y^n)). - _Paul D. Hanna_, Dec 01 2018
%F L.g.f.: -log(Product_{ k>0 } (1-2*x^k)) = Sum_{ n>=0 } (a(n)/n)*x^n. - _Benedict W. J. Irwin_, Jun 23 2016
%F G.f.: Sum_{k>=1} 2^k*x^k/(1 - x^k)^2. - _Ilya Gutkovskiy_, Oct 24 2018
%t Table[CoefficientList[Series[-Log[-QPochhammer[2, x]], {x, 0, 60}], x][[n]] (n - 1), {n, 1, 60}] (* _Benedict W. J. Irwin_, Jun 23 2016 *)
%o (PARI) a(n) = sumdiv(n, d, d*2^(n/d)); \\ _Michel Marcus_, Jul 01 2016
%Y Cf. A054599, A054600, A054601, A000016, A000031.
%Y Cf. A322200.
%K nonn
%O 0,2
%A _N. J. A. Sloane_, Apr 16 2000
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