@article{Spătaru_2023, title={Runs of Consecutive Integers Having the Same Number of Divisors}, volume={6}, url={https://journals.calstate.edu/pump/article/view/3621}, abstractNote={<p>Our objective is to provide an upper bound for the length ℓ<em><sub>N </sub></em>of the longest run of consecutive integers smaller than <em>N</em> which have the same number of divisors. We prove in an elementary way that log ℓ<em><sub>N </sub><<</em> (log <em>N</em> log log <em>N</em>)<sup>λ</sup>, where λ=1/2. Using estimates for the Jacobsthal function, we then improve the result to λ=1/3.</p>}, journal={The PUMP Journal of Undergraduate Research}, author={Spătaru, Vlad-Titus}, year={2023}, month={Feb.}, pages={96-101} }