Number of triples $(a, b, c)$ with $1 \leq a,b,c \leq n$ which are coprime ($gcd(a,b,c)=1$)

Question

Number of ordered triples $(a, b, c)$ with $gcd(a, b, c) = 1$ and $1 \leq a, b, c \leq n$ can be computed using the following formula: $$ C(n) = \sum_{k=1}^n\mu(k) \left \lfloor \frac{n}{k} \right \rfloor^3 $$, where $\mu(n)$ is Moebius function.

But how it can be derived?

Thanks!