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

Proof
We have that:

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

where $p$ denotes a prime number.

So:

Thus:
 * $\map \phi {1\,000\,000} = 400\,000$