TY - JOUR
AU - Vlad-Titus Spătaru
PY - 2023/02/02
Y2 - 2023/12/09
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 -
UR - https://journals.calstate.edu/pump/article/view/3621
AB - 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.
ER -