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

Proof
We have that:

From Euler Phi Function of Prime Power:
 * $\phi \left({p^n}\right) = p^n \left({1 - \dfrac 1 p}\right)$

Thus:

and:

From Euler Phi Function is Multiplicative:

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