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On a Problem by Erd\H{o}s and Mirsky on the ratio of the number of divisors of consecutive integers https://arxiv.org/abs/2504.11463 #mathNT

On a Problem by Erdős and Mirsky on the ratio of the number of divisors of consecutive integers

Let $\mathcal{L}$ 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 $\mathcal{L}$.

arXiv.org
April 18, 2025 at 3:10 AM · · feed2toot · 0 · 0 · 1
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