One of the recursive formulas relating values of mobious function is
$$\sum_{m \leq n} \left\lfloor \dfrac {n}{m} \right\rfloor  \mu (m) = 1.$$
But inorder to find the
 $\mu(n)$ we need to know the mobious values for $m < n $. Hence
$$\mu (n) =1-\sum_{m < n} \left \lfloor \dfrac {n}{m}\right \rfloor \mu (m) .$$
Still you are dividing $n$ by the smaller  positive integers $<n$ but you dont have to know if they are factors of $n$ .
Refer https://projecteuclid.org/euclid.mjms/1513306829 for the proof of the formula.