  Given a germ of an analytic variety $X$ and a germ of a holomorphic function
$f$ with a stratified isolated singularity with respect to the logarithmic
stratification of $X$, we show that under certain conditions on the singularity
type of the pair $(f,X)$, the following relative analog of the well known K.
Saito's theorem holds true: equality of the relative Milnor and Tjurina numbers
of f with respect to X (also known as Bruce-Roberts numbers) is equivalent to
the relative quasihomogeneity of the pair $(f,X)$, i.e. to the existence of a
coordinate system such that both $f$ and $X$ are quasihomogeneous with respect
to the same positive rational weights.
