I've got a question how to start the proof of the following task:
$$\phi(n)=\sum_{k=1}^{n-1} \left\lfloor\frac{1}{\operatorname{gcd}(n,k)} \right\rfloor$$
Any hints where and how to start? I know the definition
$$\phi(n):=\sum_{\substack{m=1\\(m,n)=1}}^n 1$$ but I don't know how to move on. Any help would be fine.
Greetings.