  The Nash multiplicity sequence was defined by M. Lejeune-Jalabert as a
non-increasing sequence of integers attached to a germ of a curve inside a germ
of a hypersurface. M. Hickel generalized this notion and described a sequence
of blow ups which allows us to compute it and study its behavior.
  In this paper, we show how this sequence can be used to compute some
invariants that appear in algorithmic resolution of singularities.
