Euler Phi Function of 42

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

 * $\phi \left({42}\right) = 12$

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

Proof
From Euler Phi Function of Square-Free Integer:
 * $\displaystyle \phi \left({n}\right) = \prod_{\substack {p \mathop \backslash n \\ p \mathop > 2} } \left({p - 1}\right)$

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

We have that:
 * $42 = 2 \times 3 \times 7$

and so is square-free.

Thus: