Euler Phi Function of 825

Example of Use of Euler $\phi$ Function

 * $\map \phi {825} = 400$

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

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

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

We have that:
 * $825 = 3 \times 5^2 \times 11$

Thus: