Maybe this is a well-know problem.

What do we know about distribution of the sequence $\bigl (\frac{\phi(n)}{n}\bigr )_{n=1}^{\infty}$ in $[0,1]$? (Where $\phi$ is the Euler's totient function).

In the other words does there exist a distribution like $\mu$ concentrated on $[0,1]$ that for every interval $[a,b]$ we have the following equation?

$$\lim_{n\to \infty} \frac{\# \ \{i \ |\ \frac{\phi(i)}{i} \in [a,b], \ 1\leq i \leq n \}}{n} = \mu([a,b]) $$

Is the sequence equidistributed in $[0,1]$?