2017 AIME I Problem 12

Call a set S product-free if there do not exist a, b, c \in S (not necessarily distinct) such that a b=c. For example, the empty set and the set \{16,20\} are product-free, whereas the sets \{4,16\} and \{2,8,16\} are not product-free. Find the number of product-free subsets of the set \{1,2,3,4,5,6,7,8,9,10\}.