Squarefree counting function ($Q(x)$)

The squarefree counting function is $Q(x)=\#\{n\le x:n\text{ is squarefree}\}$. The Möbius function gives $Q(x)={\sum }_{d\le \sqrt{x}}\mu (d)\lfloor x/d^2\rfloor$, because ${\sum }_{d^2\mid n}\mu (d)$ is the indicator of a square-free integer.