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

Author

Ilya Gutkovskiy, May 04 2017

Keywords

• nonn

Examples

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

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

Crossrefs

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

Programs

Mathematica

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

Formula

G.f.: 1/(1 - Sum_{k>=1} x^A026424(k)).