On page 83 of the pdf-file of Old and New Problems and Results in Combinatorial Number Theory, the following is asked: If we have an infinite sequence of positive integers and set to be the number of indices such that , do we then have ? In the following very short article I answer the finite version of this question, which also implies an affirmative answer to the original question: Sequences with bounded lcm for consecutive elements . I conjecture that the term is superfluous, but to get rid of it completely, a more detailed approach is needed. By the way, the constant is best possible, in the sense that it is possible to construct an infinite sequence such that, for every and infinitely many , we have .

## Sequences with bounded lcm for consecutive elements

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