A353188 Number of partitions of n that contain at least one composite part.

0, 0, 0, 0, 1, 1, 3, 4, 8, 12, 19, 27, 41, 56, 80, 109, 150, 199, 268, 350, 461, 596, 771, 984, 1258, 1589, 2007, 2514, 3145, 3905, 4846, 5973, 7356, 9010, 11020, 13418, 16315, 19756, 23890, 28788, 34639, 41548, 49767, 59441, 70899, 84354, 100221, 118803, 140645, 166153, 196035, 230853, 271512

Offset: 0

Author

Omar E. Pol, Jun 22 2022

Keywords

• nonn

Examples

			For n = 6 the partitions of 6 that contain at least one composite parts are [6], [4, 2] and [4, 1, 1]. There are three of these partitions so a(6) = 3.
		

Crossrefs

Cf. A000041, A002096, A002808, A023895, A034891, A047967, A085642, A086543, A116449, A144300, A204389.

Programs

PARI

a(n) = my(nb=0); forpart(p=n, if (#select(x->((x>1) && !isprime(x)), Vec(p)) >=1, nb++);); nb; \\ Michel Marcus, Jun 23 2022

Formula

a(n) = A000041(n) - A034891(n).