table of values of the Möbius function and the Mertens function

The following table lists the values of the Möbius function $\mu (n)$ and the Mertens function $M(n)$ for . The Möbius function is defined as $\mu (n)={(-1)}^{\omega (n)}$ (where $\omega (n)$ is the number of distinct prime factors function) for squarefree numbers, and $\mu (n)=0$ for any integer with a repeated prime factor. The Mertens function is the matching summatory function for the Möbius function,

$$M(n)=\sum _{i=1}^n\mu (i).$$