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arXiv · 2504.11463

On a Problem by Erd\H{o}s and Mirsky on the ratio of the number of divisors of consecutive integers

Jan-Christoph Schlage-Puchta
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Abstract

Let $\mathcal{L}$ be the closure of the set of all real numbers $\alpha$, such that there exist infinitely many integers $n$, such that $\alpha=\log\frac{d(n+1)}{d(n)}$, where $d$ is the number of divisors of $n$. We give improved lower bounds for the density of $\mathcal{L}$.

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Jan-Christoph Schlage-Puchta. 2025-03-31. 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

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