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, \ldots, 7, 8, 9, 10\}.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.