A328776 Product_{n>=1} (1 + x^n)^a(n) = 1 + Sum_{n>=1} sigma(n) * x^n, where sigma = A000203.

1, 3, 1, 3, -3, 2, -1, 4, 3, -8, -1, 6, 3, -4, -7, 12, 1, -6, 7, 0, -13, -13, 27, 13, -19, -11, 11, -21, -25, 191, -81, -300, 89, 327, 325, -745, -275, 579, -255, 1287, -453, -2075, -583, 2142, 5985, -6698, -6661, 6981, 3045, 3857, -7205, -2784, -5447, -4891, 48547

Offset

1,2

Comments

Inverse weigh transform of A000203.

Links

Table of n, a(n) for n=1..55.

Mathematica

b[n_, i_] := b[n, i] = If[n == 0, 1, If[i < 1, 0, Sum[Binomial[a[i], j] b[n - i j, i - 1], {j, 0, n/i}]]]; a[n_] := a[n] = DivisorSigma[1, n] - b[n, n - 1]; Array[a, 55]

Crossrefs

Cf. A000203, A192065, A320780.

Sequence in context: A336575 A050306 A205453 * A110629 A119979 A143149

Adjacent sequences: A328773 A328774 A328775 * A328777 A328778 A328779

Keyword

sign

Author

Ilya Gutkovskiy, Oct 27 2019

Status

approved