

A116450


Number of partitions of n such that the numbers of prime and composite parts differ at least by 1.


2



0, 1, 1, 2, 2, 3, 3, 6, 6, 11, 10, 18, 20, 30, 35, 49, 55, 77, 92, 120, 145, 184, 221, 283, 340, 423, 511, 627, 755, 928, 1112, 1348, 1611, 1942, 2314, 2787, 3303, 3948, 4673, 5564, 6562, 7794, 9158, 10821, 12689, 14946, 17484, 20540, 23949, 28036, 32631
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OFFSET

1,4


COMMENTS

a(n) = A002865(n)  A116449(n).


LINKS

Table of n, a(n) for n=1..51.


EXAMPLE

n=9: there are 8 partitions of 9 with parts > 1: 9, 7+2, 6+3,
5+4, 5+2+2, 4+3+2, 3+3+3 and 3+2+2+2; two of them have an equal number
of prime and composite parts: 3+2*3 and 5+2*2, therefore A116449(9)=2
and a(9)=82=6.


CROSSREFS

Sequence in context: A238786 A238547 A325681 * A054172 A236971 A121211
Adjacent sequences: A116447 A116448 A116449 * A116451 A116452 A116453


KEYWORD

nonn


AUTHOR

Reinhard Zumkeller, Feb 16 2006


STATUS

approved



