Download PDFOpen PDF in browserCurrent versionProperties of the Robin’s InequalityEasyChair Preprint 3708, version 12Versions: 12345678910111213141516171819202122232425262728293031323334353637383940414243444546474849505152→history 6 pages•Date: August 30, 2020AbstractIn mathematics, the Riemann hypothesis is a conjecture that the Riemann zeta function has its zeros only at the negative even integers and complex numbers with real part $\frac{1}{2}$. Many consider it to be the most important unsolved problem in pure mathematics. The Robin's inequality consists in $\sigma(n) < e^{\gamma } \times n \times \ln \ln n$ where $\sigma(n)$ is the divisor function and $\gamma \approx 0.57721$ is the EulerMascheroni constant. The Robin's inequality is true for every natural number $n > 5040$ if and only if the Riemann hypothesis is true. We prove the Robin's inequality is true for every natural number $n > 5040$ when $n$ is not divisible by $3$ and/or $5$ or when $n$ is not divisible by $3$ and/or $7$. Keyphrases: Divisor, inequality, number theory
