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A355195
Number of partitions of n that do not contain odd primes as parts.
1
1, 1, 2, 2, 4, 4, 7, 7, 12, 13, 20, 21, 32, 34, 49, 53, 75, 81, 112, 121, 164, 179, 237, 258, 339, 371, 478, 525, 669, 735, 927, 1019, 1272, 1403, 1734, 1912, 2348, 2591, 3153, 3484, 4213, 4655, 5595, 6183, 7387, 8171, 9706, 10731, 12692, 14035, 16515, 18266
OFFSET
0,3
FORMULA
a(n) = A000041(n) - A355193(n).
EXAMPLE
For n = 6 the partitions of 6 that do not contain odd primes as parts are [6], [4, 2], [2, 2, 2], [4, 1, 1], [2, 2, 1, 1], [2, 1, 1, 1, 1] and [1, 1, 1, 1, 1, 1]. There are seven of these partitions so a(6) = 7.
PROG
(PARI) a(n) = my(nb=0); forpart(p=n, if (#select(x->((x>2) && isprime(x)), Vec(p)) == 0, nb++); ); nb; \\ Michel Marcus, Jun 24 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
Omar E. Pol, Jun 23 2022
STATUS
approved