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A355193
Number of partitions of n that contain at least one odd prime as a part.
1
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
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
KEYWORD
nonn
AUTHOR
Omar E. Pol, Jun 23 2022
EXTENSIONS
More terms from Michel Marcus, Jun 23 2022
STATUS
approved