The lcm(1,2,...,n) as a product of sine values sampled over the points in Farey sequences

2009/09/10 by Peter Luschny, Luschny, Peter, Stefan Wehmeier +1
Mathematics · #11A05 #11B57 (Secondary) #33B10 (Primary) #Advanced Mathematical Identities #Advanced Mathematical Theories #Analytic Number Theory Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Number Theory (math.NT) #math.CA #math.NT #msc:11A05 #msc:11B57 #msc:33B10

paper · pdf · doi:10.48550/arxiv.0909.1838

4 pages

arxiv created 2009/09/10 · openalex publication_date 2009/09/10 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Recently Greg Martin derived an interesting formula for the least common multiple of 1,2,...,n. Here, we give an exposition of a concise proof in terms of the sine function.

Related

• On the distribution of lcm of k-tuples and related problems
• On the least common multiple of shifted powers
• Generalized LCM matrices
• Nair's and Farhi's identities involving the least common multiple of binomial coefficients are equivalent
• On the error term of the logarithm of the lcm of a quadratic sequence