A286226 Number of compositions (ordered partitions) of n into parts with an odd number of prime divisors (counted with multiplicity).

1, 0, 1, 1, 1, 3, 2, 6, 7, 10, 18, 22, 39, 54, 81, 127, 179, 282, 412, 620, 940, 1384, 2106, 3129, 4698, 7062, 10531, 15856, 23695, 35541, 53304, 79773, 119723, 179262, 268748, 402832, 603484, 904821, 1355652, 2031963, 3045374, 4563604, 6840316, 10250612, 15363248, 23024904, 34506390

Offset

0,6

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^A026424(k)).

Example

a(5) = 3 because we have [5], [3, 2] and [2, 3].

Mathematica

nmax = 46; CoefficientList[Series[1/(1 - Sum[Boole[OddQ[PrimeOmega[k]]] x^k, {k, 1, nmax}]), {x, 0, nmax}], x]

Crossrefs

Cf. A026424, A286218, A286222, A286224, A286227.

Sequence in context: A026211 A021310 A230267 * A269852 A329691 A293204

Adjacent sequences: A286223 A286224 A286225 * A286227 A286228 A286229

Keyword

nonn

Author

Ilya Gutkovskiy, May 04 2017

Status

approved