

A194345


Numbers n for which the largest prime factor of p(n) divides p(1)*p(2)*...*p(n1), where p(n) is the number of partitions of n.


0



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

1,2


COMMENTS

It appears that for all n > 180, the largest prime factor of p(n) does not divide p(1)*p(2)*...*p(n1). This has been checked up to n = 2000.
See A071963 and A194259 for links and additional comments.


LINKS

Table of n, a(n) for n=1..23.


EXAMPLE

1 is in the sequence because p(1) = 1 and 1 has no prime factor, so the condition is vacuously true.
For n = 7, 8, 9, 10, 11, 12, 14, 15, 16, 17, 18, 19, 21, 24, 33, 38, 39, 82, 97, every prime factor of p(n) divides p(1)*p(2)*...*p(n1).
For n = 158, 166, 180, not every prime factor of p(n) divides p(1)*p(2)*...*p(n1), but the largest one does.


CROSSREFS

Cf. A000041, A071963, A087173, A192885, A194259, A194260, A194261, A194262.
Sequence in context: A065808 A250046 A062947 * A120208 A100562 A115841
Adjacent sequences: A194342 A194343 A194344 * A194346 A194347 A194348


KEYWORD

nonn


AUTHOR

Jonathan Sondow, Aug 21 2011


STATUS

approved



