A210469 a(n) = n - primepi(2n).

0, 0, 0, 0, 1, 1, 1, 2, 2, 2, 3, 3, 4, 5, 5, 5, 6, 7, 7, 8, 8, 8, 9, 9, 10, 11, 11, 12, 13, 13, 13, 14, 15, 15, 16, 16, 16, 17, 18, 18, 19, 19, 20, 21, 21, 22, 23, 24, 24, 25, 25, 25, 26, 26, 26, 27, 27, 28, 29, 30, 31, 32, 33, 33, 34, 34, 35, 36, 36, 36

Offset

1,8

Comments

The number of distinct odd composite parts appearing in the partitions of 2n into two parts.

a(n) is the number of odd composite numbers up to 2*n-1. - Michel Marcus, Aug 05 2023

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..10000

Index entries for sequences related to partitions

Formula

a(n) = n - primepi(2n).

Example

a(6) = 1 since 9 is the only odd composite number appearing in the partitions of 2*6 = 12 into two parts. For example, 12 = (1+11) = (2+10) = (3+9) = (4+8) = (5+7) = (6+6). Note that the numbers in the partitions with identical parts are counted only once.

Maple

with(numtheory);  a:=n->n-pi(2*n);  seq(a(k), k=1..70);

Mathematica

Table[n - PrimePi[2 n], {n, 70}] (* Robert G. Wilson v, Jan 24 2013 *)

Prog

(PARI) a(n) = n - primepi(2*n); \\ Michel Marcus, Aug 05 2023

Crossrefs

Cf. A099802.

See A224710 for a closely related sequence.

Sequence in context: A194251 A029114 A224710 * A073174 A107631 A029098

Adjacent sequences: A210466 A210467 A210468 * A210470 A210471 A210472

Keyword

nonn,easy

Author

Wesley Ivan Hurt, Jan 24 2013

Status

approved