A set of positive integers is called weakly triple-free if, for any integer x, the set {x, 2x, 3x}⊈S. For example, all subsets of {1, 2, 3, 4, 5} are weakly triple-free except {1, 2, 3}, {1, 2, 3, 4}, {1, 2, 3, 5}, and {1, 2, 3, 4, 5} (since each of these contains the subset {1, 2, 3} The numbers of weakly triple-free subsets of {1, 2, ..., n} for n = 0, 1, 2, ... are 1, 2, 4, 7, 14, 28, 50, 100, 200, 360, 720, ... (OEIS A068060).
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