A118168 a(n) = x for which abs(x^x-n!) is minimal.
1, 1, 1, 2, 3, 3, 4, 5, 6, 6, 7, 8, 9, 10, 10, 11, 12, 13, 14, 14, 15, 16, 17, 18, 18, 19, 20, 21, 22, 22, 23, 24, 25, 26, 27, 27, 28, 29, 30, 31, 32, 32, 33, 34, 35, 36, 37, 37, 38, 39, 40, 41, 42, 42, 43, 44, 45, 46, 47, 47, 48, 49, 50, 51, 52, 52, 53, 54, 55, 56, 57, 57, 58, 59
Offset: 0
Examples
3! = 6, the closest x^x can get to 6 is 2^2, so a(3) = 2