A234716 Number of odd composite integers k, such that n-1 < k < 2n-2.

0, 0, 0, 0, 0, 1, 1, 1, 2, 1, 1, 2, 2, 3, 4, 3, 3, 4, 5, 5, 6, 5, 5, 6, 6, 6, 7, 6, 7, 8, 8, 8, 9, 9, 9, 9, 9, 9, 10, 10, 10, 11, 11, 12, 13, 12, 13, 14, 15, 14, 15, 14, 14, 15, 15, 14, 15, 14, 15, 16, 17, 18, 19, 19, 19, 19, 19, 20, 21, 20, 20, 21, 22, 23

Offset: 1

Author

Wesley Ivan Hurt, Dec 29 2013

Keywords

• nonn
• easy

Comments

Number of partitions of 2n into two odd parts such that the largest part is an odd composite less than 2n-2.

Examples

			a(9) = 2; There are two partitions of 2(9) = 18 into two odd parts such that the largest part is an odd composite less than 2(9)-2 = 16: (15,3) and (9,9).
		

Links

• Index entries for sequences related to partitions

Crossrefs

Cf. A002375, A141100.

Programs

Maple

with(numtheory); A234716:=n->floor((n-1)/2) - pi(2*n-3) + pi(n-1); seq(A234716(n), n=1..100);

Mathematica

Table[Floor[(n - 1)/2] - PrimePi[2 n - 3] + PrimePi[n - 1], {n, 100}]

Formula

a(n) = floor((n-1)/2) - pi(2n-3) - pi(n-1).