Corresponding values of factorials are 1! (and 2!), 4!, 5!, 8!, 9!, 11! and 13!, respectively.

This sequence is complete by Saunders, Theorem 2.

More generally, Saunders, Theorem 2 states that, for any positive integers a, b, c, m with gcd(b, c) = 1, there are only finitely many solutions to phi(a*n!/b) = cx^m and these solutions satisfy n <= max {61, 3a, 3b, 3c}.