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Let each of the positive integers $a_1 ,\dots, a_n$ be less than $m$ such that the least common multiple of any two of the positive integers $a_1 ,\dots, a_n$ is greater than the integer $m$.

Then what is the best possible upper bound for $\sum_{j=1}^n\frac 1{a_j}$? (I'm only aware of the upper bound $2$ but perhaps read somewhere that $6/5$ also serve as a bound)

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