  We analyze the number N of functionally independent generalized Casimir
invariants for non-semisimple Lie algebras \frak{s}\overrightarrow{%
oplus}_{R}\frak{r} with Levi factors isomorphic to \frak{so}(3) and
\frak{sl}(2,R) in dependence of the pair (R,\frak{r}) formed by a
representation R of \frak{s} and a solvable Lie algebra \frak{r}. We show that
for any dimension n >= 6 there exist Lie algebras
\frak{s}\overrightarrow{\oplus}_{R}\frak{r} with non-trivial Levi decomposition
such that N(\frak{s}% \overrightarrow{oplus}_{R}\frak{r}) = 0.
