Geodesic
A Sum of Reciprocals of Least Common Multiples
Canadian mathematical bulletin, Tome 21 (1978) no. 1, pp. 117-118

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The purpose of this note is to prove the following theorem conjectured by P. Erdös.Theorem. Let a0, a1, ..., ak be integers satisfying 1 ≤ a0 a1 ... k, and let [ai-1 ai] denote the least common multiple of ai-1 and ai Then 1 with equality occurring if and only if ai = 2i for 1 ≤ i ≤ k. 
Borwein, D. A Sum of Reciprocals of Least Common Multiples. Canadian mathematical bulletin, Tome 21 (1978) no. 1, pp. 117-118. doi: 10.4153/CMB-1978-019-7
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