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Erdős problem 539

For ∣A∣=n|A| = n, how small can the cofactor set Q(A)={a/gcd⁡(a,b):a,b∈A}Q(A) = \{a / \gcd(a,b) : a, b \in A\} be? The answer is h(n)=n1/2+o(1)h(n) = n^{1/2 + o(1)}: a new upper bound h(n)≤n1/2exp⁡(O(log⁡n))h(n) \le n^{1/2} \exp(O(\sqrt{\log n})) matches the classical lower bound.

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