A344446 - OEIS

%I #20 Oct 12 2023 15:51:56

%S 0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,1,1,2,1,1,1,3,2,3,2,2,3,3,4,4,2,3,5,

%T 7,5,4,4,5,6,7,7,6,6,7,10,10,7,7,9,10,11,11,13,13,8,12,14,14,13,9,13,

%U 14,16,17,19,15,15,15,22,23,15,14,19,23,23,22,24

%N Number of partitions of n into 3 semiprimes.

%H Alois P. Heinz, <a href="/A344446/b344446.txt">Table of n, a(n) for n = 0..20000</a>

%F a(n) = [x^n y^3] 1/Product_{j>=1} (1-y*x^A001358(j)).

%p h:= proc(n) option remember; `if`(n=0, 0,

%p      `if`(numtheory[bigomega](n)=2, n, h(n-1)))

%p     end:

%p b:= proc(n, i) option remember; series(`if`(n=0, 1, `if`(i<1, 0,

%p      `if`(i>n, 0, x*b(n-i, h(min(n-i, i))))+b(n, h(i-1)))), x, 4)

%p     end:

%p a:= n-> coeff(b(n, h(n)), x, 3):

%p seq(a(n), n=0..80);

%t Table[Count[IntegerPartitions[n,{3}],_?(PrimeOmega[#]=={2,2,2}&)],{n,0,80}] (* _Harvey P. Dale_, Oct 12 2023 *)

%Y Column k=3 of A344447.

%Y Cf. A001358.

%K nonn,look

%O 0,19

%A _Alois P. Heinz_, May 19 2021