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Erdős problem 539

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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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Problem row
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Metadata
sha256:18b6f8735146e49e8fadfdb1bea009af71bc57db098d79db49c01f8ffb22dde7
Observation
sha256:9c8326e865b6017b103af7611c852a06776d81964979b8ab5a1b800cd550dff6
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sha256:fbb11dc4be060b58ecaa43494090f2b0b938c6bc869fa9dede16d3482ddf8c9c
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sha256:a956b84c437202e5a02cc9e036a621bd14a302b34a75758115730bdbb77c52a4
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sha256:a4a96441668a9f8b33afbcb3f696a2639f5fae145f36ddc063d7f67d5fb87ce8
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36c6d0fef71a3fec84d9dcd5eeca4e22e378f7cb
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