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Multiple-Free Set

A set of positive integers is called weakly k-multiple-free if, for any integer x, the set {x,2x,3x,...,kx} !subset= S.

A set of positive integers is called strongly k-multiple-free if x in S implies 2x not in S, 3x not in S, ..., kx not in S.

See also

Double-Free Set, Sum-Free Set, Triple-Free Set

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Cite this as:

Weisstein, Eric W. "Multiple-Free Set." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Multiple-FreeSet.html