Euler Phi Function/Examples/1,000,000/Proof 2

Proof
We have that:

From Euler Phi Function of Integer:
 * $\displaystyle \phi \left({n}\right) = n \prod_{p \mathop \backslash n} \left({1 - \frac 1 p}\right)$

where $p$ denotes a prime number.

So:

Thus:
 * $\phi \left({1\,000\,000}\right) = 400\,000$