A116450 Number of partitions of n such that the numbers of prime and composite parts differ by at least 1.

0, 1, 1, 2, 2, 3, 3, 6, 6, 11, 10, 18, 20, 30, 35, 49, 55, 77, 92, 120, 145, 184, 221, 283, 340, 423, 511, 627, 755, 928, 1112, 1348, 1611, 1942, 2314, 2787, 3303, 3948, 4673, 5564, 6562, 7794, 9158, 10821, 12689, 14946, 17484, 20540, 23949, 28036, 32631

Offset: 1

Author

Reinhard Zumkeller, Feb 16 2006

Keywords

• nonn

Comments

a(n) = A002865(n) - A116449(n).

Examples

			n=9: there are 8 partitions of 9 with parts > 1: 9, 7+2, 6+3,
5+4, 5+2+2, 4+3+2, 3+3+3 and 3+2+2+2; two of them have an equal number
of prime and composite parts: 3+2*3 and 5+2*2, therefore A116449(9)=2
and a(9)=8-2=6.