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?

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?

Erdős [Er35] proved that this sum always converges for a primitive set. Lichtman [Li23] proved that the answer is yes. An alternative, simpler, proof is given by Alexeev, Barreto, Li, Lichtman, Price, Shah, Tang, and Tao [ABLLPSTT26].