A282135 - OEIS

%I #6 Feb 07 2017 09:03:54

%S 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,

%T 12,21,27,27,21,18,24,30,36,36,25,27,36,49,48,36,36,51,51,54,57,66,63,

%U 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

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

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

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

%H Ilya Gutkovskiy, <a href="/A282135/a282135.pdf">Extended graphical example</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Semiprime.html">Semiprime</a>

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

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

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

%Y Cf. A001358, A098238, A199331.

%K nonn

%O 1,14

%A _Ilya Gutkovskiy_, Feb 06 2017