A286227 Number of compositions (ordered partitions) of n into parts with an even number of prime divisors (counted with multiplicity).

1, 1, 1, 1, 2, 3, 5, 7, 10, 15, 24, 36, 53, 78, 118, 179, 271, 405, 605, 907, 1366, 2055, 3086, 4628, 6948, 10440, 15689, 23560, 35371, 53110, 79771, 119821, 179958, 270243, 405833, 609495, 915394, 1374780, 2064647, 3100680, 4656676, 6993575, 10503180, 15773877, 23689467, 35577360

Offset

0,5

Links

Amiram Eldar, Table of n, a(n) for n = 0..5000

Eric Weisstein's World of Mathematics, Prime Factor

Index entries for sequences related to compositions

Formula

G.f.: 1/(1 - Sum_{k>=1} x^A028260(k)).

Example

a(6) = 5 because we have [6], [4, 1, 1], [1, 4, 1], [1, 1, 4] and [1, 1, 1, 1, 1, 1].

Mathematica

nmax = 45; CoefficientList[Series[1/(1 - Sum[Boole[EvenQ[PrimeOmega[k]]] x^k, {k, 1, nmax}]), {x, 0, nmax}], x]

Crossrefs

Cf. A028260, A286219, A286223, A286225, A286226.

Sequence in context: A018133 A261081 A116975 * A134792 A300795 A033068

Adjacent sequences: A286224 A286225 A286226 * A286228 A286229 A286230

Keyword

nonn

Author

Ilya Gutkovskiy, May 04 2017

Status

approved