  We study the asymptotic behavior of the counting function of tensor products
of operators, in the cases where the factors are either pseudodifferential
operators on closed manifolds, or pseudodifferential operators of Shubin type
on $\mathbb{R}^n$, respectively. We obtain, in particular, the sharpness of the
remainder term in the corresponding Weyl formulae, which we prove by means of
the analysis of some explicit examples.
