  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.
