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

0,11

Comments

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

Links

Table of n, a(n) for n=0..64.

Eric Weisstein's World of Mathematics, Semiprime

Index entries for sequences related to compositions

Formula

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

Example

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

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]

Crossrefs

Cf. A001222, A001358, A023360, A101048.

Sequence in context: A300722 A087625 A300720 * A154574 A119493 A355344

Adjacent sequences: A280235 A280236 A280237 * A280239 A280240 A280241

Keyword

nonn

Author

Ilya Gutkovskiy, Dec 29 2016

Status

approved