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, 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

Offset: 0

Author

William Rex Marshall, Jul 28 2011

Keywords

• nonn

Comments

From Franklin T. Adams-Watters, Jul 28 2011: (Start)

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.

It appears that this sequence is O(n). (End)

Examples

			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.
		

Links

• William Rex Marshall, Pascal program

Crossrefs

Cf. A000142, A157017.