Let $r (n)$ count the number of $d_{1}, d_{2}$ such that $d_{1} ∣ n$ and $d_{2} ∣ n$ and $d_{1} < d_{2} < 2 d_{1}$ . Is it true that, for every $ϵ > 0$ , $r (n) < ϵ τ (n)$ for almost all $n$ , where $τ (n)$ is the number of divisors of $n$ ?

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number theory · solved · possible · 0 attempts

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