A286225 Number of compositions (ordered partitions) of n into parts with an even number of distinct prime divisors.

1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 7, 9, 13, 18, 25, 34, 46, 61, 83, 112, 153, 209, 286, 387, 526, 713, 969, 1317, 1794, 2437, 3312, 4497, 6110, 8302, 11290, 15347, 20865, 28354, 38533, 52361, 71167, 96721, 131464, 178672, 242834, 330020, 448532, 609590, 828511, 1126037, 1530418, 2079977, 2826896, 3841998

Offset

0,7

Links

Amiram Eldar, Table of n, a(n) for n = 0..7000

Eric Weisstein's World of Mathematics, Distinct Prime Factors

Index entries for sequences related to compositions

Formula

G.f.: 1/(1 - Sum_{k>=1} x^A030231(k)).

Example

a(8) = 4 because we have [6, 1, 1], [1, 6, 1], [1, 1, 6] and [1, 1, 1, 1, 1, 1, 1, 1].

Mathematica

nmax = 53; CoefficientList[Series[1/(1 - Sum[Boole[EvenQ[PrimeNu[k]]] x^k, {k, 1, nmax}]), {x, 0, nmax}], x]

Crossrefs

Cf. A030231, A285798, A286221, A286224.

Sequence in context: A320316 A236166 A017834 * A239048 A219898 A263360

Adjacent sequences: A286222 A286223 A286224 * A286226 A286227 A286228

Keyword

nonn

Author

Ilya Gutkovskiy, May 04 2017

Status

approved