Let $A = {a_{1} < a_{2} < \dots} \subseteq N$ be infinite and let $A (x)$ count the number of indices for which $lcm (a_{i}, a_{i + 1}) \leq x$ . Is it true that $A (x) ≪ x^{1/2}$ ? How large can $lim inf \frac{A ( x )}{x ^{1/2}}$ be?

Worked, still open.

number theory · solved · 0 attempts

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