On a Problem by Erdős and Mirsky on the ratio of the number of divisors of consecutive integersLet $\mathcal{L}$ be the closure of the set of all real numbers $α$, such that there exist infinitely many integers $n$, such that $α=\log\frac{d(n+1)}{d(n)}$, where $d$ is the number of divisors of $n$. We give improved lower bounds for the density of $\mathcal{L}$.
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