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arXiv · 2505.00727

Ratios of consecutive values of the divisor function

Sean Eberhard
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Abstract

We show that the sequence of ratios $d(n+1) / d(n)$ of consecutive values of the divisor function attains every positive rational infinitely many times. This confirms a prediction of Erd\H{o}s.

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Sean Eberhard. 2025-04-27. Ratios of consecutive values of the divisor function. https://doi.org/10.1016/j.jnt.2025.10.002

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