A116450 Number of partitions of n such that the numbers of prime and composite parts differ by at least 1.

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

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)=8-2=6.

Crossrefs

Sequence in context: A238786 A238547 A325681 * A054172 A236971 A373446

Adjacent sequences: A116447 A116448 A116449 * A116451 A116452 A116453

Keyword

nonn

Author

Reinhard Zumkeller, Feb 16 2006

Status

approved