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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
1, 7, 8, 9, 10, 11, 12, 14, 15, 16, 17, 18, 19, 21, 24, 33, 38, 39, 82, 97, 158, 166, 180
OFFSET
1,2
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.
EXAMPLE
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.
KEYWORD
nonn,more
AUTHOR
Jonathan Sondow, Aug 21 2011
STATUS
approved