Euler Phi Function/Examples/1,000,000

Example of Use of Euler $\phi$ Function
The value of the Euler $\phi$ function for the integer $1\,000\,000$ is $400\,000$.

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