A226982 a(n) = ceiling(n/2) - primepi(n).

1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 5, 5, 5, 5, 5, 5, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 10, 10, 11, 11, 11, 11, 12, 12, 13, 13, 13, 13, 13, 13, 14, 14, 15, 15, 15

Offset: 1

Author

Wesley Ivan Hurt, Jun 25 2013

Keywords

• nonn
• easy

Comments

The number of partitions of 2n into exactly two parts such that the smaller part is an odd composite integer, n > 1.

Sequence decreases by 1 when n is an even prime and increases by 1 when n is an odd composite. - Wesley Ivan Hurt, Dec 27 2013

Examples

			a(18) =2. 2*18=38 has two partitions into exactly two odd parts with smallest part composite: (27,9) and (21,15). - _Wesley Ivan Hurt_, Dec 27 2013
		

Links

• Index entries for sequences related to partitions

Crossrefs

Cf. A000720, A004526, A002375, A141100.

Programs

Maple

seq(ceil(n/2)-numtheory[pi](n),n=1..100);

Formula

a(n) = floor((n+1)/2) - pi(n) = A004526(n+1) - A000720(n).

a(n) = n - A004526(n) - A000720(n). - Wesley Ivan Hurt, Dec 27 2013