A116450 - OEIS

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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

(list; graph; refs; listen; history; text; internal format)

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.