FI-MO 2013 Problem 4

A subset $E$ of the set $\{1,2,3,\ldots,50\}$ is said to be special if it does not contain any pair of the form $\{x,3x\}.$ A special set $E$ is superspecial if it contains as many elements as possible. How many element there are in a superspecial set and how many superspecial sets there are?