  We consider a model for a Z'-boson coupled only to baryon minus lepton number
and hypercharge. Besides the usual right-handed neutrinos, we add a pair of
fermions with a fractional lepton charge, which we therefore call leptinos. One
of the leptinos is taken to be odd under an additional Z_2 charge, the other
even. This allows for a natural (inverse) seesaw mechanism for neutrino masses.
The odd leptino is a candidate for dark matter, but has to be resonantly
annihilated by the Z'-boson or the Higgs-boson responsible for giving mass to
the former. Considering collider and cosmological bounds on the model, we find
that the Z'-boson and/or the extra Higgs-boson can be seen at the LHC. With
more pairs of leptinos leptogenesis is possible.
