A363492 Numbers k such that the partition number p(k) = A000041(k) can be written as a product of smaller partition numbers.
0, 1, 7, 8, 9, 10, 11, 12, 14, 15, 16, 17, 18, 19, 21, 24, 39
Offset: 1
Examples
0 and 1 are terms, because p(0) = p(1) = 1 is the empty product. 7 is a term, because p(7) = 15 = 3*5 = p(3)*p(4). 39 is a term, because p(39) = 31185 = 3^4*385 = p(3)^4*p(18). 33 is not a term, even though all prime factors of p(33) = 3^2 * 7^2 * 23 appear in smaller partition numbers. (In particular, 33 is a term of A194345.) This is because the only smaller partition number that is divisible by 23 is p(32) = 3 * 11^2 * 23, but p(33) is not divisible by 11.
Comments