A100950 Number of partitions of n into a coprime pair of a prime and a semiprime.

0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 3, 0, 2, 1, 1, 1, 5, 0, 2, 1, 2, 2, 4, 0, 3, 3, 5, 3, 4, 0, 2, 4, 4, 2, 4, 1, 5, 6, 3, 3, 6, 1, 4, 4, 6, 5, 4, 2, 4, 4, 7, 6, 6, 3, 3, 6, 7, 6, 4, 1, 3, 10, 7, 5, 7, 3, 6, 9, 6, 5, 5, 5, 4, 7, 8, 7, 7, 4, 6, 9, 8, 9, 4, 3, 7, 8, 8, 9, 8, 2, 4, 10, 11, 10, 6, 8, 7, 12, 9, 8, 6, 6, 5

Offset: 1

Author

Reinhard Zumkeller, Nov 23 2004

Keywords

• nonn

Comments

A100951(n)<=a(n)<=A100949(n)<=Min{A000720(n), A072000(n)}.

a(n) = A000040(i) + A001358(j) for some i and j, such that A000040(i) is not a factor of A001358(j).

Examples

			A100949(21) = #{7+2*7, 11+2*5, 17+2*2} = 3,
a(21) = #{11+2*5, 17+2*2} = 2.