A355195 Number of partitions of n that do not contain odd primes as parts.
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
Keywords
Examples
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.
Programs
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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