Euler Phi Function of Square-Free Integer

Theorem
Let $n$ be an integer such that $n \ge 2$.

Let $n$ be square-free.

Let $\map \phi n$ be the Euler $\phi$ function of $n$.

That is, let $\map \phi n$ be the count of strictly positive integers less than or equal to $n$ which are prime to $n$.

Then:
 * $\map \phi n = \displaystyle \prod_{\substack {p \mathop \divides n \\ p \mathop > 2} } \paren {p - 1}$

where $p \divides n$ denotes the primes which divide $n$.