Abstract:A set of integers greater than 1 is primitive if no member in the set divides another. Erdős proved in 1935 that the series
$f(A) = \sum _{a\in A}1/(a \log a)$
is uniformly bounded over all choices of primitive sets A. In 1986, he asked if this bound is attained for the set of prime numbers. In this article, we answer in the affirmative.
As further applications of the method, we make progress towards a question of Erdős, Sárközy and Szemerédi from 1968. We also refine the class… Show more
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