# Euler Phi Function of 6

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

$\map \phi 6 = 2$

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

## Proof

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

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

We have that:

$6 = 2 \times 3$

and so is square-free.

Thus:

 $\displaystyle \map \phi 6$ $=$ $\displaystyle \paren {3 - 1}$ $\displaystyle$ $=$ $\displaystyle 2$

$\blacksquare$