Ratios of consecutive values of the divisor function
arXiv:2505.00727 · doi:10.1016/j.jnt.2025.10.002
Abstract
We show that the sequence of ratios of consecutive values of the divisor function attains every positive rational infinitely many times. This confirms a prediction of Erdős.
arXiv comment3 pp. Accepted version. To appear in the Journal of Number Theory