Runs of Consecutive Integers Having the Same Number of Divisors

Authors

  • Vlad-Titus Spătaru Liceul Teoretic Internațional de Informatică București

DOI:

https://doi.org/10.46787/pump.v6i0.3621

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.

Downloads

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

Issue

Vol. 6 (2023): PUMP Journal of Undergraduate Research

Section

Articles

License

The author(s) will retain the copyright, but by submitting the article agree to grant permission to the PUMP Journal of Undergraduate Research to publish, distribute, and archive the article. The author(s) will acknowledge prior publication in the PUMP Journal of Undergraduate Research for all future uses of the article or parts of it.