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

0,4

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)

Links

Sharvil Kesarwani, Table of n, a(n) for n = 0..168

Thomas Bloom, Problem 390, Erdős Problems.

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