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Erdős Problem 538 #778

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@mo271

What is the conjecture

https://www.erdosproblems.com/538

Let $r\geq 2$ and suppose that $A\subseteq\{1,\ldots,N\}$ is such that, for any $m$, there are at most $r$ solutions to $m=pa$ where $p$ is prime and $a\in A$. Give the best possible upper bound for
$$\sum_{n\in A}\frac{1}{n}.$$

Status: open

Choose either option

  • I plan on working on this conjecture
  • This issue is up for grabs: I would like to see this conjecture added by somebody else

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