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
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
KEYWORD
nonn,easy
AUTHOR
Wesley Ivan Hurt, Jan 24 2013
STATUS
approved