Runs of Consecutive Integers Having the Same Number of Divisors
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. Retrieved from https://journals.calstate.edu/pump/article/view/3621
Section
Articles
Copyright (c) 2023 Vlad-Titus Spătaru
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