Two elementary formulae and some complicated properties for Mertens function

Two elementary formulae for Mertens function $M(n)$ are obtained. With these formulae, $M(n)$ can be calculated directly and simply, which can be easily implemented by computer. $M(1)\sim M(2\times {10}^7)$ are calculated one by one. Based on these $2\times {10}^7$ samples, some of the complicated properties for Mertens function $M(n)$, its 16479 zeros, the 10043 local maximum/minimum between two neighbor zeros, and the relation with the cumulative sum of the squarefree integers, are understood numerically and empirically.