  Partition functions for M2-brane theories in various backgrounds are
computed. We consider in particular configurations of membranes at orbifold
singularities preserving N=5 or N=6 supersymmetry. The worldvolume membrane
theory for some of these configurations has been recently constructed in terms
of N=6 Chern-Simons theories. The detailed structure of the partition functions
as well as their transformation rules under the R-symmetry are explicitly
computed using the Plethystic Programme.
