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arXiv · 2003.12166

A generalization of primitive sets and a conjecture of Erdős

Tsz Ho Chan·Jared Duker Lichtman·Carl Pomerance
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Abstract

A set of integers greater than 1 is primitive if no element divides another. Erdős proved in 1935 that the sum of $1/(n \log n)$ for $n$ running over a primitive set $A$ is universally bounded over all choices for $A$. In 1988 he asked if this universal bound is attained by the set of prime numbers. We answer the Erdős question in the affirmative for 2-primitive sets. Here a set is 2-primitive if no element divides the product of 2 other elements.

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Tsz Ho Chan, Jared Duker Lichtman, Carl Pomerance. 2020-09-21. A generalization of primitive sets and a conjecture of Erdős. https://doi.org/10.19086/da.17290

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