

A226982


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


0



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
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OFFSET

1,15


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


LINKS

Table of n, a(n) for n=1..67.
Index entries for sequences related to partitions


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


EXAMPLE

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


MAPLE

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


CROSSREFS

Cf. A000720, A004526, A002375, A141100.
Sequence in context: A051742 A134119 A064661 * A280952 A235122 A131996
Adjacent sequences: A226979 A226980 A226981 * A226983 A226984 A226985


KEYWORD

nonn,easy


AUTHOR

Wesley Ivan Hurt, Jun 25 2013


STATUS

approved



