A045772 a[ n ] such that a[ n ]^b is the best fit to n! with a[ n ]>=b.

1, 2, 2, 3, 2, 3, 4, 6, 5, 4, 7, 9, 5, 7, 10, 9, 11, 3, 6, 12, 11, 4, 3, 2, 14, 5, 12, 4, 14, 9, 18, 23, 17, 5, 24, 8, 12, 25, 28, 11, 26, 19, 18, 27, 36, 18, 5, 9, 34, 22, 32, 26, 9, 17, 29, 23, 12, 43, 6, 47, 38, 16, 32, 16, 45, 16, 30, 43, 12, 57, 37, 29, 28, 26, 15, 6, 24, 44