g(n) ≪_ε n^{ρ+ε} with ρ = (13 - √69)/10 < 0.47 for multiplicative Sidon sets that intersect every interval of length L up to n.
Erdős,On Some Applications of Graph Theory to Number Theoretic Problems, Publ
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Gaps in Multiplicative Sidon Sets
g(n) ≪_ε n^{ρ+ε} with ρ = (13 - √69)/10 < 0.47 for multiplicative Sidon sets that intersect every interval of length L up to n.