SMO 2005 Problem 1

An integer is square-free if it is not divisible by $a^2$ for any integer $a>1$ . Let $S$ be the set of positive square-free integers. Determine, with justification, the value of$$\sum_{k\epsilon S}\left[\sqrt{\frac{10^{10}}{k}}\right]$$where $[x]$ denote the greatest integer less than or equal to $x$