On the number of Mobius $\mu =0$ numbers less than a given number.

Question

How many of the composite numbers are multiples of squares:

Let $C(n) =$ all composite numbers $\le n$

Let $\mu_0(n) =$ the number of integers $\le n$ with a value of $\mu =0$

$${\mu_0(n) \over C(n)} \thicksim (??) $$