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

Proof
We have that:

From Euler Phi Function of Prime Power:
 * $\map \phi {p^n} = p^n \paren {1 - \dfrac 1 p}$

Thus:

and:

From Euler Phi Function is Multiplicative:

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