In this paper we give an interpretation of the invariants λa,i(A) introduced by Lyubeznik in [Lyu93] for a reasonably general class of singularities. In positive characteristic it is the newly introduced class of close to F -rational varieties and the invariants are described in terms of étale cohomology with Z/pZ-coefficients. This result presents the first application of Emerton and Kisin's Riemann-Hilbert type correspondence to local algebra. In fact our proof works in characteristic zero as well so that we obtain generalizations of results on these invariants which were previously obtained for isolated singularities by analytic techniques.