A300277 G.f.: 1 + Sum_{n>=1} a(n)*x^n/(1 - x^n) = Product_{n>=1} 1/(1 - n*x^n).

1, 2, 5, 11, 24, 48, 96, 184, 348, 645, 1169, 2140, 3761, 6687, 11645, 20326, 34635, 59854, 100579, 171211, 285718, 479325, 791315, 1318955, 2156805, 3553589, 5783306, 9445861, 15250215, 24759156, 39713787, 63991400, 102197851, 163548416, 259744930, 413761633, 653715967

Offset: 1

Author

Ilya Gutkovskiy, Mar 01 2018

Keywords

• nonn

Comments

Moebius transform of A006906.

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 1..6000
• N. J. A. Sloane, Transforms

Crossrefs

Cf. A000837, A006906, A078374, A085410, A300274, A300275, A300276, A300278.

Programs

Mathematica

nn = 37; f[x_] := 1 + Sum[a[n] x^n/(1 - x^n), {n, 1, nn}]; sol = SolveAlways[0 == Series[f[x] - Product[1/(1 - n x^n), {n, 1, nn}], {x, 0, nn}], x]; Table[a[n], {n, 1, nn}] /. sol // Flatten
s[n_] := SeriesCoefficient[Product[1/(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, 37}]

Formula

a(n) = Sum_{d|n} mu(n/d)*A006906(d).