Lyubeznik's invariants for cohomologically isolated singularities

In this note I give a description of Lyubeznik's local cohomology invariants for a certain natural class of local rings, namely the ones which have the same local cohomology vanishing as one expects from an isolated singularity. This strengthens our results of [Manuel Blickle, Raphael Bondu, Local cohomology multiplicities in terms of étale cohomology, Ann. Inst. Fourier 55 (7) (2005)] while at the same time somewhat simplifying the proofs. Through examples I further point out the bad behavior of these invariants under reduction mod p.