Phi Euler

Euler's totient function counts the positive integers up to a given integer $n$ that are relatively prime to $n$. Formally, it can be defined as the number of integers $k$ in the range $1\le k\le n$ for which $gcd(n,k)=1$. Euler's product formula states

$\phi \left(n\right)=n\prod _{p|n}\left(1-\frac{1}{p}\right)$

For a prime number $p$ and for an integer $k$, this expression reduces to

$\phi \left(p^k\right)=p^k\left(1-\frac{1}{p}\right)$

phi_euler(Integer)

Description

Given an integer $n$, returns $\phi \left(n\right)$.