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Is the factorization of $a_m-a_n$ affected by the fact that $\Sigma \frac{1}{a_k}<+\infty$?
I would like to ask the following.
Let $(a_n)$ be a sequence of natural numbers such that
$\sum_{k=1}^{\infty}\frac{1}{a_k}$ converges. Is it true that for
infinitely many $m$, there is a $n<m$ ...
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