Euler Phi Function of 30

Example of Euler $\phi$ Function of Square-Free Integer

 * $\map \phi {30} = 8$

where $\phi$ denotes the Euler $\phi$ Function.

Proof
From Euler Phi Function of Square-Free Integer:
 * $\ds \map \phi n = \prod_{\substack {p \mathop \divides n \\ p \mathop > 2} } \paren {p - 1}$

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

We have that:
 * $30 = 2 \times 3 \times 5$

and so is square-free.

Thus: