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(k(n))! lcm (1, 2,..., n)> (n - 1) !

Source: 2020 Estonia TST 2.1

November 18, 2020
number theoryleast common multiplefactorial

Problem Statement

For every positive integer xx, let k(x)k(x) denote the number of composite numbers that do not exceed xx. Find all positive integers nn for which (k(n))!(k (n))! lcm (1,2,...,n)>(nāˆ’1)!(1, 2,..., n)> (n - 1) ! .
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