A194345 Numbers k for which the largest prime factor of p(k) divides p(1)*p(2)*...*p(k-1), where p(k) is the number of partitions of k.

1, 7, 8, 9, 10, 11, 12, 14, 15, 16, 17, 18, 19, 21, 24, 33, 38, 39, 82, 97, 158, 166, 180

Offset: 1

Author

Jonathan Sondow, Aug 21 2011

Keywords

• nonn
• more

Comments

It appears that for all k > 180, the largest prime factor of p(k) does not divide p(1)*p(2)*...*p(k-1). This has been checked up to k = 2000. [Checked up to k = 10000, using A071963 b-file. - Pontus von Brömssen, Jun 05 2023]

See A071963 and A194259 for links and additional comments.

Examples

			1 is in the sequence because p(1) = 1 and 1 has no prime factor, so the condition is vacuously true.
For k = 7, 8, 9, 10, 11, 12, 14, 15, 16, 17, 18, 19, 21, 24, 33, 38, 39, 82, 97, every prime factor of p(k) divides p(1)*p(2)*...*p(k-1).
For k = 158, 166, 180, not every prime factor of p(k) divides p(1)*p(2)*...*p(k-1), but the largest one does.
		

Crossrefs

Cf. A000041, A071963, A087173, A192885, A194259, A194260, A194261, A194262.