A disproof of the Riemann Hypothesis via the Nicolas Criterion

Abstract: The achievement of this paper is a confutation of the inequality addressed by the Nicolas criterion for the Riemann Hypothesis, carried out after establishing properties of two related sequences. One of them is the product $\prod_{k=1}^n(1-1/p_k)$, rewritten as an alternating sum. The disproof is by contradiction: assuming the Nicolas inequality is always true, we reach an absurdity exploiting the aforementioned properties and a general lemma.