# Translated sums of primitive sets

@inproceedings{Lichtman2021TranslatedSO, title={Translated sums of primitive sets}, author={Jared D. Lichtman}, year={2021} }

The Erdős primitive set conjecture states that the sum f(A) = ∑ a∈A 1 a log a , ranging over any primitive set A of positive integers, is maximized by the set of prime numbers. Recently Laib, Derbal, and Mechik proved that the translated Erdős conjecture for the sum f(A, h) = ∑ a∈A 1 a(log a+h) is false starting at h = 81, by comparison with semiprimes. In this note we prove that such falsehood occurs already at h = 1.04 · · · , and show this translate is best possible for semiprimes. We also…

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