Erdős Problem #164

A set $A\subset \mathbb{N}$ is primitive if no member of $A$ divides another. Is the sum\[\sum_{n\in A}\frac{1}{n\log n}\]maximised over all primitive sets when $A$ is the set of primes?

#164: [Er76g][Er86]

number theory | primitive sets

Erdős [Er35] proved that this sum always converges for a primitive set. Lichtman [Li23] proved that the answer is yes.

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Related OEIS sequences: A137245

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Additional thanks to: Jared Lichtman

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