Euler Phi Function of Square-Free Integer

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

Let $n$ be square-free.

Let $\phi \left({n}\right)$ be the Euler $\phi$ function of $n$.

That is, let $\phi \left({n}\right)$ be the count of strictly positive integers less than or equal to $n$ which are prime to $n$.

Then:
 * $\displaystyle \phi \left({n}\right) = \prod_{\substack {p \mathop \backslash n \\ p \mathop > 2} } \left({p - 1}\right)$

where:
 * $p$ ranges over all primes
 * $\backslash$ denotes divisibility.