New results on the least common multiple of consecutive integers

DOI10.1090/S0002-9939-08-09730-XzbMath1229.11007arXiv0808.1507OpenAlexW2007333777MaRDI QIDQ3629412

Bakir Farhi, Daniel M. Kane

Publication date: 27 May 2009

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0808.1507

zbMATH Keywords

least common multiplearithmetic functionexact period

Mathematics Subject Classification ID

Special sequences and polynomials (11B83) Arithmetic functions; related numbers; inversion formulas (11A25) Multiplicative structure; Euclidean algorithm; greatest common divisors (11A05)

Related Items (19)

On the least common multiple of several consecutive values of a polynomial ⋮ Further results on a curious arithmetic function ⋮ NOTES ON A CURIOUS ARITHMETIC FUNCTION ⋮ The least common multiple of consecutive terms in a cubic progression ⋮ Newton representation of functions over natural integers having integral difference ratios ⋮ Integral Difference Ratio Functions on Integers ⋮ Uniform lower bound for the least common multiple of a polynomial sequence ⋮ The least common multiple of a sequence of products of linear polynomials ⋮ A note on proving the strong NP-hardness of a scheduling problem with position dependent job processing times ⋮ Asymptotic behavior of the least common multiple of consecutive arithmetic progression terms ⋮ Note on the lower bound of least common multiple ⋮ New lower bounds for the least common multiples of arithmetic progressions ⋮ The general case on the order of appearance of product of consecutive Fibonacci and Lucas numbers ⋮ Further improvements of lower bounds for the least common multiples of arithmetic progressions ⋮ The least common multiple of consecutive arithmetic progression terms ⋮ New lower bounds for the least common multiple of polynomial sequences ⋮ On the lcm-analog of binomial coefficient ⋮ On the periodicity of some Farhi arithmetical functions ⋮ THE LEAST COMMON MULTIPLE OF CONSECUTIVE TERMS IN A QUADRATIC PROGRESSION

Cites Work

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• Lower bounds for the least common multiple of finite arithmetic progressions
• On the periodicity of an arithmetical function
• Nontrivial lower bounds for the least common multiple of some finite sequences of integers
• Nontrivial lower bounds for the least common multiple of some sequences of integers.
• Improvements of lower bounds for the least common multiple of finite arithmetic progressions
• On Chebyshev-Type Inequalities for Primes
• The least common multiple of a quadratic sequence
• A Limit Involving Least Common Multiples: 10797
• On the Product of the Primes

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