Euler's Totient Function

Euler's totient function (also called the Phi function) counts the number of positive integers less than $n$ that are coprime to $n$. That is

$$\varphi (n)=\mathrm{card}\left\{m\in \mathbb{N}\mid 1\le m<n\text{ and }\gcd (m,n)=1\right\}$$

We can calculate $\varphi (n)$ via this formula

$$\varphi (n)=n\left(1-\frac{1}{p_1}\right)\left(1-\frac{1}{p_2}\right)\cdots \left(1-\frac{1}{p_k}\right)$$

where $p_1,p_2,\dots ,p_k$ are the distinct primes dividing $n$