One of the recursive formulas relating 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 $$\mu (n) =1-\sum_{m < n} \left \lfloor \dfrac {n}{m}\right \rfloor \mu (m) .$$ Refer https://www.google.com/url?sa=t&source=web&rct=j&url=https://projecteuclid.org/euclid.mjms/1513306829&ved=2ahUKEwj55dn6gp7jAhVRsaQKHbFFAYQQFjAAegQIAhAB&usg=AOvVaw1RHQeEpc3qyIf1xFpkWkgY for the proof of the formula.
Hunde Eba
- 11
- 2