A112020 Number of partitions of n into distinct semiprimes.

1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 2, 0, 0, 1, 2, 2, 1, 0, 1, 3, 2, 2, 1, 2, 3, 5, 2, 2, 3, 5, 4, 5, 3, 4, 6, 9, 6, 5, 6, 10, 10, 9, 7, 9, 12, 14, 12, 11, 14, 18, 17, 16, 16, 19, 21, 24, 21, 23, 26, 29, 30, 32, 31, 33, 39, 40, 39, 41, 45, 49, 54, 53, 54, 59, 68, 66, 68, 70, 78, 82, 88, 86, 93, 101

Offset: 0

Author

Reinhard Zumkeller, Aug 26 2005

Keywords

• nonn

Examples

			For n=4 one partition: {2*2}.
For n=6 one partition: {2*3}.
For n=10 two partitions: {2*2+2*3,2*5}.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A101048, A112022, A001358, A000586.

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; `if`(n=0, 1, `if`(i<1, 0,
      b(n-i, h(min(n-i, i-1)))+b(n, h(i-1))))
    end:
a:= n-> b(n, h(n)):
seq(a(n), n=0..100);  # Alois P. Heinz, Mar 19 2024

Mathematica

nmax = 100;
CoefficientList[Series[Product[1+x^(Prime[j] Prime[k]), {j, 1, nmax}, {k, j, nmax}], {x, 0, nmax}], x] (* Jean-François Alcover, Nov 10 2021 *)