The Erdős primitive set conjecture states that the sum , ranging over any primitive set 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 is false starting at , by comparison with semiprimes. In this note we prove that such falsehood occurs already at , and show this translate is best possible for semiprimes. We also obtain results for translated sums of -almost primes with larger .
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Jared Duker Lichtman 1
@article{CRMATH_2022__360_G4_409_0, author = {Jared Duker Lichtman}, title = {Translated sums of primitive sets}, journal = {Comptes Rendus. Math\'ematique}, pages = {409--414}, publisher = {Acad\'emie des sciences, Paris}, volume = {360}, year = {2022}, doi = {10.5802/crmath.285}, language = {en}, }
Jared Duker Lichtman. Translated sums of primitive sets. Comptes Rendus. Mathématique, Volume 360 (2022), pp. 409-414. doi : 10.5802/crmath.285. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.285/
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