A282135 Expansion of (Sum_{k = p*q, p prime, q prime} x^k)^3.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 3, 0, 3, 3, 4, 6, 6, 3, 9, 9, 12, 12, 6, 10, 15, 18, 16, 12, 12, 21, 27, 27, 21, 18, 24, 30, 36, 36, 25, 27, 36, 49, 48, 36, 36, 51, 51, 54, 57, 66, 63, 42, 57, 75, 72, 66, 51, 69, 78, 79, 90, 102, 73, 75, 84, 117, 126, 84, 75, 105, 123, 121, 114, 120, 124, 102, 117, 156, 156, 129

Offset: 1

Author

Ilya Gutkovskiy, Feb 06 2017

Keywords

• nonn

Comments

Number of ways to write n as an ordered sum of three semiprimes (A001358).

Conjecture: a(n) > 0 for n > 15.

Examples

			a(14) = 3 because we have [6, 4, 4], [4, 6, 4] and [4, 4, 6].
		

Links

• Ilya Gutkovskiy, Extended graphical example
• Eric Weisstein's World of Mathematics, Semiprime

Crossrefs

Cf. A001358, A098238, A199331.

Programs

Mathematica

nmax = 83; Rest[CoefficientList[Series[Sum[Floor[PrimeOmega[k]/2] Floor[2/PrimeOmega[k]] x^k, {k, 2, nmax}]^3, {x, 0, nmax}], x]]

Formula

G.f.: (Sum_{k = p*q, p prime, q prime} x^k)^3.