OBM 2015 Problem 2

Consider $S=\{1, 2, 3, \cdots, 6n\}$ , $n>1$ . Find the largest $k$ such that the following statement is true: every subset $A$ of $S$ with $4n$ elements has at least $k$ pairs $(a,b)$ , $a<b$ and $b$ is divisible by $a$ .