ILL 1992 Problem 11

Let $\phi(n,m), m \neq 1$ , be the number of positive integers less than or equal to $n$ that are coprime with $m.$ Clearly, $\phi(m,m) = \phi(m)$ , where $\phi(m)$ is Euler's phi function. Find all integers $m$ that satisfy the following inequality: $$\frac{\phi(n,m)}{n} \geq \frac{\phi(m)}{m}$$ for every positive integer $n.$