A Beautiful Equivalence of the Riemann Hypothesis (The Riemann Hypothesis and Young´s Lattice [Part 1/9])

This article presents a novel, elementary and direct equivalent formulation of the famous Riemann Hypothesis. This work proposes that this hypothesis is true if and only if a specific inequality relating a simple analytical series to the sum-of-divisors function of $n$, $\sigma(n) = \sum_{d|n} d$, holds for all positive integers $n$. The equivalence, stated in the Theorem 7, allows to establish directly the hypothesis as a fine, elemental and rigorous bounding of the function $\sigma(n)$ for all positive integers $n$. This approach offering an accessible and potential pathway to attack it. The explicit equivalence is given by:

The Riemann Hypothesis is equivalent to:
$$
\sum_{k \in \mathbb{N}} \frac{\left(\frac{1}{1}+\dots+\frac{1}{n}\right)^k}{k!} \textstyle \Big(\frac{1}{k}+\dots+\frac{1}{k^2}\Big) > \displaystyle \sum_{d|n} d
$$
for all $n \in \mathbb{N}$.