TY - JOUR
AU - Spătaru, Vlad-Titus
PY - 2023/02/02
Y2 - 2024/08/13
TI - Runs of Consecutive Integers Having the Same Number of Divisors
JF - The PUMP Journal of Undergraduate Research
JA - PUMP J. Undergrad. Res.
VL - 6
IS - 0
SE - Articles
DO - 10.46787/pump.v6i0.3621
UR - https://journals.calstate.edu/pump/article/view/3621
SP - 96-101
AB - <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>
ER -