Runs of Consecutive Integers Having the Same Number of Divisors

  • Vlad-Titus Spătaru Liceul Teoretic Internațional de Informatică București
Keywords: divisor counting function; consecutive equidivisible integers

Abstract

Our objective is to provide an upper bound for the length ℓN 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 ℓN << (log N log log N)λ, where λ=1/2. Using estimates for the Jacobsthal function, we then improve the result to λ=1/3.

Published
2023-02-02
How to Cite
Spătaru, V.-T. (2023). Runs of Consecutive Integers Having the Same Number of Divisors. The PUMP Journal of Undergraduate Research, 6, 96-101. https://doi.org/10.46787/pump.v6i0.3621