Ratios of consecutive values of the divisor function

2025/04/27 by Eberhard, Sean
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2505.00727

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 Erdős.

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