A355193 Number of partitions of n that contain at least one odd prime as a part.

0, 0, 0, 1, 1, 3, 4, 8, 10, 17, 22, 35, 45, 67, 86, 123, 156, 216, 273, 369, 463, 613, 765, 997, 1236, 1587, 1958, 2485, 3049, 3830, 4677, 5823, 7077, 8740, 10576, 12971, 15629, 19046, 22862, 27701, 33125, 39928, 47579, 57078, 67788, 80963, 95852, 114023

Offset

0,6

Links

Table of n, a(n) for n=0..47.

Formula

a(n) = A000041(n) - A355195(n).

Example

For n = 6 the partitions of 6 that contain at least one odd prime as a part are [3, 3], [5, 1], [3, 2, 1], [3, 1, 1, 1]. There are four of these partitions so a(6) = 4.

Prog

(PARI) a(n) = my(nb=0); forpart(p=n, if (#select(x->((x>2) && isprime(x)), Vec(p)) >=1, nb++); ); nb; \\ Michel Marcus, Jun 23 2022

Crossrefs

Cf. A000041, A065091, A235945, A353188, A355195.

Sequence in context: A115264 A210631 A212543 * A238546 A147617 A308910

Adjacent sequences: A355190 A355191 A355192 * A355194 A355195 A355196

Keyword

nonn

Author

Omar E. Pol, Jun 23 2022

Extensions

More terms from Michel Marcus, Jun 23 2022

Status

approved