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Beautiful set

Source: IMAR 2017, Problem 3

November 18, 2017
Problem Setscombinatorics

Problem Statement

We consider SS a set of odd positive interger numbers with n≥3n\geq 3 elements such that no element divides another element. We say that a set SS is beautifulbeautiful if for any 3 elements from SS, there is one the divides the sum of the other 2. We call a beautiful set SS maximalmaximal if we can't add another number to the set such that SS will still be beautiful. Find the values of nn for which there exists a maximalmaximal set.
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