A344446 Number of partitions of n into 3 semiprimes.

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

Offset: 0

Author

Alois P. Heinz, May 19 2021

Keywords

• nonn
• look

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..20000

Crossrefs

Column k=3 of A344447.

Cf. A001358.

Programs

Maple

h:= proc(n) option remember; `if`(n=0, 0,
     `if`(numtheory[bigomega](n)=2, n, h(n-1)))
    end:
b:= proc(n, i) option remember; series(`if`(n=0, 1, `if`(i<1, 0,
     `if`(i>n, 0, x*b(n-i, h(min(n-i, i))))+b(n, h(i-1)))), x, 4)
    end:
a:= n-> coeff(b(n, h(n)), x, 3):
seq(a(n), n=0..80);

Mathematica

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

Formula

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