

A226983


a(n) = ceiling(n/2)  pi(2n) + pi(n1).


1



0, 1, 0, 0, 1, 1, 1, 2, 2, 1, 2, 2, 3, 4, 4, 3, 4, 5, 5, 6, 6, 5, 6, 6, 7, 7, 7, 7, 8, 8, 8, 9, 10, 9, 10, 9, 9, 10, 11, 10, 11, 11, 12, 13, 13, 13, 14, 15, 15, 15, 15, 14, 15, 15, 15, 15, 15, 15, 16, 17, 18, 19, 20, 19, 20, 19, 20, 21, 21, 20, 21, 22, 23, 24
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OFFSET

1,8


COMMENTS

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


LINKS

Muniru A Asiru, Table of n, a(n) for n = 1..1000
Index entries for sequences related to partitions


FORMULA

a(n) = floor((n+1)/2)  ( pi(2n)  pi(n1) ) = A004526(n+1)  A035250(n).


MAPLE

with(numtheory); seq(ceil(k/2)(pi(2*k)pi(k1)), k=1..100);


MATHEMATICA

Table[Floor[(n + 1) / 2]  (PrimePi[2 n]  PrimePi[n  1]), {n, 100}] (* Vincenzo Librandi, Dec 07 2016 *)


PROG

(PARI) a226983(n) = if(n==1, 0, ceil(n/2)  primepi(2*n) + primepi(n1)) \\ Michael B. Porter, Jun 29 2013


CROSSREFS

Cf. A000720, A004526, A035250.
Sequence in context: A109831 A247352 A097266 * A112175 A112206 A038541
Adjacent sequences: A226980 A226981 A226982 * A226984 A226985 A226986


KEYWORD

sign,easy


AUTHOR

Wesley Ivan Hurt, Jun 25 2013


STATUS

approved



