IL-GILLIS 2013 Problem 2

Let $A=\{n\in\mathbb{Z}\mid 0<n<2013\}$ . A subset $B\subseteq A$ is called reduced if for any two numbers $x,y\in B$ , we must have $x\cdot y \notin B$ . For example, any subset containing the numbers $3,5,15$ cannot be reduced, and same for a subset containing $4,16$ .

[list=a] [] Find the maximal size of a reduced subset of $A$ . [] How many reduced subsets are there with that maximal size? [/list]