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

0,7

Links

Table of n, a(n) for n=0..52.

Formula

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

Example

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.

Prog

(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

Crossrefs

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

Sequence in context: A076136 A064188 A229990 * A147620 A195746 A088953

Adjacent sequences: A353185 A353186 A353187 * A353189 A353190 A353191

Keyword

nonn

Author

Omar E. Pol, Jun 22 2022

Status

approved