Euler Phi Function of 315

Example of Use of Euler $\phi$ Function

 * $\map \phi {315} = 144$

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

Proof
From Euler Phi Function of Integer:
 * $\displaystyle \map \phi n = n \prod_{p \mathop \divides n} \paren {1 - \frac 1 p}$

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

We have that:
 * $315 = 3^2 \times 5 \times 7$

Thus: