A305632 Expansion of Product_{r = 1 or not a perfect power} 1/(1 + (-x)^r).

1, 1, 0, 1, 2, 2, 1, 2, 4, 3, 2, 4, 6, 5, 4, 7, 10, 8, 7, 11, 15, 13, 12, 17, 22, 19, 18, 25, 30, 28, 26, 35, 42, 39, 38, 49, 59, 56, 54, 69, 81, 77, 76, 94, 110, 105, 105, 127, 147, 141, 142, 171, 195, 189, 190, 227, 257, 250, 254, 299, 335, 328, 334, 390, 432

Offset

0,5

Links

Table of n, a(n) for n=0..64.

Example

O.g.f.: 1/((1 - x)(1 + x^2)(1 - x^3)(1 - x^5)(1 + x^6)(1 - x^7)(1 + x^10)...).

Mathematica

nn=20;
radQ[n_]:=Or[n==1, GCD@@FactorInteger[n][[All, 2]]==1];
ser=Product[1/(1+(-x)^p), {p, Select[Range[nn], radQ]}];
Table[SeriesCoefficient[ser, {x, 0, n}], {n, 0, nn}]

Crossrefs

Cf. A000607, A001597, A005117, A007916, A048165, A081362, A091050, A280954, A303707, A304779, A304817, A305614, A305630-A305635.

Sequence in context: A368415 A370075 A144963 * A329069 A035374 A229219

Adjacent sequences: A305629 A305630 A305631 * A305633 A305634 A305635

Keyword

nonn

Author

Gus Wiseman, Jun 07 2018

Status

approved