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A194345 Numbers n for which the largest prime factor of p(n) divides p(1)*p(2)*...*p(n-1), 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 (list; graph; refs; listen; history; text; internal format)
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(n-1). 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(n-1).

For n = 158, 166, 180, not every prime factor of p(n) divides p(1)*p(2)*...*p(n-1), 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

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Last modified August 10 11:52 EDT 2020. Contains 336379 sequences. (Running on oeis4.)