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ON THE $p$-FREE ROBIN INEQUALITIES FOR $p=3,5,7 $
Keywords:
Robin inequality, Riemann hypothesisDOI:
https://doi.org/10.17654/0972555522028Abstract
In this paper, we prove the analogous inequalities for the Robin inequality for prime numbers $p=3,5,7$. That is, if $B$ is some selected positive constant, then we have the inequalities such that $\frac{\sigma(n)}{n} \leq \frac{p-1}{p} e^\gamma \log \log n+\frac{B}{\log \log n}$ for $p$-free integers $n>3$.
Received: June 2, 2022
Revised: July 10, 2022
Accepted: July 19, 2022
References
T. Oshiro and Y. Koya, An analogue of the Robin inequality of the second type for odd integers, JP Journal of Algebra, Number Theory and Applications 56 (2022), 27-36.
G. Robin, Grandes valeurs de la fonction somme des diviseurs et Hypothèse de Riemann, J. Math. Pures and Appl. 63 (1984), 187-213.
L. Schoenfeld, Sharper bounds for the Chebyshev functions $theta(x)$ and $psi(x)$ II, Math. Comp. 30(134) (1976), 337-360.
C. L. Washington and A. Yang, Analogues of the Robin-Lagarias criteria for the Riemann hypothesis, Int. J. Number Theory 17(4) (2021), 843-870.
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