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Problem #164: A set $A\subset \mathbb{N}$ is primitive if no member of...

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...

Problem Statement

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?
Categories: Number Theory Primitive Sets

Progress

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

Source: erdosproblems.com/164 | Last verified: January 13, 2026

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