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arXiv · 2301.04464

Runs of Consecutive Integers Having the Same Number of Divisors

Vlad-Titus Spătaru
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Abstract

Our objective is to provide an upper bound for the length $\ell_N$ of the longest run of consecutive integers smaller than $N$ which have the same number of divisors. We prove in an elementary way that $\log\ell_N\ll(\log N\log\log N)^\lambda$, where $\lambda=1/2$. Using estimates for the Jacobsthal function, we then improve the result to $\lambda=1/3$.

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Vlad-Titus Spătaru. 2023-01-08. Runs of Consecutive Integers Having the Same Number of Divisors. https://doi.org/10.46787/pump.v6i0.3621

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