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Farey sequence
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===Farey fractions and the least common multiple=== The [[Least common multiple|lcm]] can be expressed as the products of Farey fractions as <math display=block> \text{lcm}[1,2,...,N] = e^{\psi(N)} = \frac{1}{2} \left( \prod_{r \in F_N, 0<r \le 1/2} 2 \sin(\pi r) \right)^2 </math> where {{math|''ψ''(''N'')}} is the second [[Chebyshev function]].<ref>{{Cite arXiv |eprint = 0907.4384|last1 = Martin|first1 = Greg|title = A product of Gamma function values at fractions with the same denominator|class = math.CA|year = 2009}}</ref><ref>{{Cite arXiv |eprint=0909.1838 |last1=Wehmeier |first1=Stefan |title=The LCM(1,2,...,n) as a product of sine values sampled over the points in Farey sequences |class=math.CA |year=2009}}</ref>
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