Squarefree counting function
= Squarefree counting function
{title2=$Q(x)$}
= Squarefree-count function
{synonym}
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>.