Möbius function

For any positive integer $n$, the Möbius function $\mu(n)$ is defined as

$$\begin{gathered} \mu \left(n\right)=\left\{\begin{array}{l}-1\mathrm{if}n\mathit{}\mathrm{is}\mathrm{a}\mathrm{square}-\mathrm{free}\mathrm{positive}\mathrm{integer}\mathrm{with}\mathrm{an}\mathrm{odd}\mathrm{number}\mathrm{of}\mathrm{prime}\mathrm{factors} \\ 0\mathrm{if}n\mathit{}\mathrm{has}\mathrm{a}\mathrm{squared}\mathrm{prime}\mathrm{factor}\\ 1\mathrm{if}n\mathit{}\mathrm{is}\mathrm{a}\mathrm{square}-\mathrm{free}\mathrm{positive}\mathrm{integer}\mathrm{with}\mathrm{an}\mathrm{even}\mathrm{number}\mathrm{of}\mathrm{prime}\mathrm{factors}\end{array}\right. \end{gathered}$$

mu_moebius(Integer)

Description

Given an integer $n$, returns $\mu(n)$ as defined above.