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Found problems: 1

2016 Romania Team Selection Tests, 3
Tags: number divisors , number theory
Let $n$ be a positive integer, and let $a_1,a_2,..,a_n$ be pairwise distinct positive integers. Show that $$\sum_{k=1}^{n}{\frac{1}{[a_1,a_2,…,a_k]}} <4,$$ where $[a_1,a_2,…,a_k]$ is the least common multiple of the integers $a_1,a_2,…,a_k$.