  In this paper we define a new cohomology of a smooth manifold called
Lichnerowicz type cohomology attached to a function. Firstly, we study some
basic properties of this cohomology as: a de Rham type isomorphism, dependence
on the function, singular forms, relative cohomology, Mayer-Vietoris sequence,
homotopy invariance and next, a regular case is considered. The notions are
introduced using techniques from the study of two cohomologies of a smooth
manifold: the Lichnerowicz cohomology and the cohomology attached to a
function.
