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%I #6 Mar 01 2018 14:54:13
%S 1,1,4,5,14,19,42,57,115,170,287,433,694,1061,1709,2461,3740,5635,
%T 8243,12256,18255,26135,37826,54209,78315,110488,159418,224514,315414,
%U 442790,618665,855640,1199409,1642334,2288904,3144738,4303994,5862294,8031872,10869290,14749050
%N G.f.: 1 + Sum_{n>=1} a(n)*x^n/(1 - x^n) = Product_{n>=1} (1 + n*x^n).
%C Moebius transform of A022629.
%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%F a(n) = Sum_{d|n} mu(n/d)*A022629(d).
%t nn = 41; f[x_] := 1 + Sum[a[n] x^n/(1 - x^n), {n, 1, nn}]; sol = SolveAlways[0 == Series[f[x] - Product[(1 + n x^n), {n, 1, nn}], {x, 0, nn}], x]; Table[a[n], {n, 1, nn}] /. sol // Flatten
%t s[n_] := SeriesCoefficient[Product[(1 + k x^k), {k, 1, n}], {x, 0, n}]; a[n_] := Sum[MoebiusMu[n/d] s[d], {d, Divisors[n]}]; Table[a[n], {n, 1, 41}]
%Y Cf. A000837, A022629, A078374, A085410, A300274, A300275, A300276, A300277.
%K nonn
%O 1,3
%A _Ilya Gutkovskiy_, Mar 01 2018
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