

A193429


a(n) = minimum value of the largest element of a nonempty set of positive integers > n such that their product is equal to n!, or 0 if no such set exists.


1



1, 0, 0, 6, 24, 12, 10, 20, 16, 28, 25, 22, 33, 30, 28, 28, 39, 35, 36, 44, 44, 42, 44, 50, 50, 50, 57, 57, 56, 58, 65, 64, 64, 72, 72, 70, 75, 80, 80, 78, 80, 88, 88, 86, 88, 95, 95, 94, 96, 102, 104, 102, 104, 111, 111, 110, 112, 120, 119, 118, 120, 122, 125
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OFFSET

0,4


COMMENTS

For n > 4, there is always the factorization n! = (2*n) * (n!/(2*n)), so a(n) is only 0 for n = 1 or 2.  Franklin T. AdamsWatters, Jul 28 2011.
It appears that this sequence is O(n).  Franklin T. AdamsWatters, Jul 28 2011.


LINKS

Table of n, a(n) for n=0..62.
William Rex Marshall, Pascal program


EXAMPLE

For n=5, n! = 120. Any factorization of 120 into 3 (or more) factors will have a factor <= 5, so we take the most central factorization into two factors, 120 = 10*12, the maximum of {10, 12} is 12, thus a(5) = 12.


CROSSREFS

Cf. A000142, A157017.
Sequence in context: A293256 A213344 A337023 * A213278 A029592 A112034
Adjacent sequences: A193426 A193427 A193428 * A193430 A193431 A193432


KEYWORD

nonn


AUTHOR

William Rex Marshall, Jul 28 2011


STATUS

approved



