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

1,3

Comments

a(18) > 10000 (if it exists).

Links

Table of n, a(n) for n=1..17.

Example

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.

Crossrefs

Cf. A000041, A034878, A363636.

Except for a(1) = 0, subsequence of A194345.

Sequence in context: A250046 A062947 A194345 * A120208 A100562 A115841

Adjacent sequences: A363489 A363490 A363491 * A363493 A363494 A363495

Keyword

nonn,more

Author

Pontus von Brömssen, Jun 05 2023

Status

approved