A307779 a(1) = 1; a(n+1) = Sum_{d|n, n/d odd} a(d).

1, 1, 1, 2, 2, 3, 4, 5, 5, 7, 8, 9, 11, 12, 13, 17, 17, 18, 22, 23, 25, 31, 32, 33, 38, 41, 42, 49, 51, 52, 63, 64, 64, 74, 75, 82, 93, 94, 95, 108, 113, 114, 130, 131, 133, 155, 156, 157, 174, 179, 187, 206, 208, 209, 231, 242, 247, 271, 272, 273, 307, 308, 309, 345, 345

Offset: 1

Author

Ilya Gutkovskiy, Apr 28 2019

Keywords

• nonn

Crossrefs

Cf. A002033, A003238, A307776, A307777, A307778.

Programs

Mathematica

a[n_] := a[n] = Sum[Boole[OddQ[(n - 1)/d]] a[d], {d, Divisors[n - 1]}]; a[1] = 1; Table[a[n], {n, 1, 65}]
a[n_] := a[n] = SeriesCoefficient[x (1 + Sum[a[k] x^k/(1 - x^(2 k)), {k, 1, n - 1}]), {x, 0, n}]; Table[a[n], {n, 1, 65}]

Formula

G.f.: x * (1 + Sum_{n>=1} a(n)*x^n/(1 - x^(2*n))).

L.g.f.: log(Product_{n>=1} ((1 + x^n)/(1 - x^n))^(a(n)/(2*n))) = Sum_{n>=1} a(n+1)*x^n/n.