A280238 Expansion of 1/(1 - Sum_{k>=2} floor(bigomega(k)/2)*floor(2/bigomega(k))*x^k), where bigomega(k) is the number of prime divisors of k counted with multiplicity (A001222).

1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 3, 0, 2, 2, 6, 3, 6, 3, 11, 10, 16, 10, 23, 23, 40, 34, 52, 52, 93, 94, 130, 133, 209, 234, 330, 352, 488, 570, 804, 909, 1198, 1405, 1918, 2283, 2980, 3512, 4622, 5636, 7340, 8811, 11321, 13864, 17937, 21957, 27936, 34262, 43857, 54290, 68915, 84940, 107685, 133811, 169615, 210375, 265305

Offset: 0

Author

Ilya Gutkovskiy, Dec 29 2016

Keywords

• nonn

Comments

Number of compositions (ordered partitions) into semiprimes (A001358).

Examples

			a(10) = 3 because we have [4, 6], [6, 4] and [10].
		

Links

• Eric Weisstein's World of Mathematics, Semiprime
• Index entries for sequences related to compositions

Crossrefs

Cf. A001222, A001358, A023360, A101048.

Programs

Mathematica

nmax = 44; CoefficientList[Series[1/(1 - Sum[Floor[PrimeOmega[k]/2] Floor[2/PrimeOmega[k]] x^k, {k, 2, nmax}]), {x, 0, nmax}], x]

Formula

G.f.: 1/(1 - Sum_{k>=2} floor(bigomega(k)/2)*floor(2/bigomega(k))*x^k).