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

0,11

Links

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

Example

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}.

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 *)

Crossrefs

Cf. A101048, A112022, A001358, A000586.

Sequence in context: A205593 A277937 A334913 * A069160 A089616 A089615

Adjacent sequences: A112017 A112018 A112019 * A112021 A112022 A112023

Keyword

nonn

Author

Reinhard Zumkeller, Aug 26 2005

Status

approved