Factorial Factors |

The factorial function,
*n*! = 1^{ . }2^{ . }...^{ . }*n*,
has many interesting properties. In this problem, we want to
determine the maximum number of integer terms (excluding 1) that
can be used to express *n*!. For example:

8! = 1^{ . }2^{ . }3^{ . }4^{ . }5^{ . }6^{ . }7^{ . }8 = 2^{ . }3^{ . }2^{ . }2^{ . }5^{ . }3^{ . }2^{ . }7^{ . }2^{ . }2^{ . }2 = 2^{7 . }3^{2 . }5^{ . }7

By inspection, it is clear that the maximum number of terms (excluding 1) that can be multiplied together to produce 8! is 11.

2 1000000 1996 5 8 123456

1 3626619 5957 5 11 426566

Miguel Revilla 2004-09-16