On Values Of D(N !)/M !,Phi(N !)/M ! And Sigma(N !)/M !

For f one of the classical arithmetic functions d, phi and sigma, we establish constraints on the quadruples (n, m, a, b) of integers satisfying f(n!)/m! = a/b. In particular, our results imply that as nm tends to infinity, the number of distinct prime divisors dividing the product of the numerator and denominator of the fraction f(n!)/m!, when reduced, tends to infinity.