A300274 - OEIS

%I #6 Mar 01 2018 14:53:48

%S 2,2,6,10,22,30,62,86,146,206,342,454,726,974,1442,1962,2862,3762,

%T 5398,7094,9834,12942,17726,22938,31042,40094,53254,68518,90246,

%U 114914,150142,190550,245906,310942,398554,500474,637590,797534,1007714,1255850,1578526,1956786

%N G.f.: 1 + Sum_{n>=1} a(n)*x^n/(1 - x^n) = Product_{n>=1} (1 + x^n)/(1 - x^n).

%C Moebius transform of A015128.

%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>

%F a(n) = Sum_{d|n} mu(n/d)*A015128(d).

%t nn = 42; f[x_] := 1 + Sum[a[n] x^n/(1 - x^n), {n, 1, nn}]; sol = SolveAlways[0 == Series[f[x] - Product[(1 + x^n)/(1 - x^n), {n, 1, nn}], {x, 0, nn}], x]; Table[a[n], {n, 1, nn}] /. sol // Flatten

%t s[n_] := SeriesCoefficient[Product[(1 + x^k)/(1 - x^k), {k, 1, n}], {x, 0, n}]; a[n_] := Sum[MoebiusMu[n/d] s[d], {d, Divisors[n]}]; Table[a[n], {n, 1, 42}]

%Y Cf. A000837, A015128, A078374, A300275, A300276, A300277, A300278.

%K nonn

%O 1,1

%A _Ilya Gutkovskiy_, Mar 01 2018