Note on the Odd Perfect Numbers

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 $\frac{1}{2}$. In 2011, Sol{\'e} and and Planat stated that the Riemann Hypothesis is true if and only if $\frac{{\pi }^2}{6}\times \prod _{q\le q_n}(1+\frac{1}{q})>e^{\gamma }\times \log \theta (q_n)$ is satisfied for all primes $q_n>3$, where $\theta (x)$ is the Chebyshev function, $\gamma \approx 0.57721$ is the Euler-Mascheroni constant and $\log$ is the natural logarithm. We state the conjecture that $\frac{{\pi }^2}{6.4}\times \prod _{q\le q_n}(1+\frac{1}{q})>e^{\gamma }\times \log \theta (q_n)$ is satisfied for infinitely many prime numbers $q_n>{10}^8$. Under the assumption of this conjecture and the Riemann Hypothesis, we prove that there is not any odd perfect number at all.