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.

Full Text
Published version (Free)

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call