A300274 G.f.: 1 + Sum_{n>=1} a(n)*x^n/(1 - x^n) = Product_{n>=1} (1 + x^n)/(1 - x^n).

2, 2, 6, 10, 22, 30, 62, 86, 146, 206, 342, 454, 726, 974, 1442, 1962, 2862, 3762, 5398, 7094, 9834, 12942, 17726, 22938, 31042, 40094, 53254, 68518, 90246, 114914, 150142, 190550, 245906, 310942, 398554, 500474, 637590, 797534, 1007714, 1255850, 1578526, 1956786

Offset: 1

Author

Ilya Gutkovskiy, Mar 01 2018

Keywords

• nonn

Comments

Moebius transform of A015128.

Links

• N. J. A. Sloane, Transforms

Crossrefs

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

Programs

Mathematica

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
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}]

Formula

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