A set of positive integers is called weakly k-multiple-free if, for any integer x, the set {x, 2x, 3x, ..., k x}⊈S. A set of positive integers is called strongly k-multiple-free if x element S implies 2x not element S, 3x not element S, ..., k x not element S.

double-free set | sum-free set | triple-free set