• Corpus ID: 239024869

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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TLDR
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Note on translated sum on primitive sequences
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  • 2021
In this note, we construct a new set \boldsymbol{S} of primitive sets such that for any real number x\geq 60 we get: \begin{equation*} \sum\limits_{a\in \mathcal{A}}\frac{1}{a(\log
Somme translatée sur des suites primitives et la conjecture d'Erdös
The Erdős conjecture for primitive sets
<p>A subset of the integers larger than 1 is <italic>primitive</italic> if no member divides another. Erdős proved in 1935 that the sum of <inline-formula content-type="math/mathml"> <mml:math
Note on translated sum on primitive sequences
  • Notes on Number Theory and Discrete Mathematics
  • 2021
prime product formula, dissected, Integers 21A (2021)
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