  We analyze a class of entangled states for bipartite $d \otimes d$ systems,
with $d$ non-prime. The entanglement of such states is revealed by the
construction of canonically associated entanglement witnesses. The structure of
the states is very simple and similar to the one of isotropic states: they are
a mixture of a separable and a pure entangled state whose supports are
orthogonal. Despite such simple structure, in an opportune interval of the
mixing parameter their entanglement is not revealed by partial transposition
nor by the realignment criterion, i.e. by any permutational criterion in the
bipartite setting. In the range in which the states are Positive under Partial
Transposition (PPT), they are not distillable; on the other hand, the states in
the considered class are provably distillable as soon as they are Nonpositive
under Partial Transposition (NPT). The states are associated to any set of more
than two pure states. The analysis is extended to the multipartite setting. By
an opportune selection of the set of multipartite pure states, it is possible
to construct mixed states which are PPT with respect to any choice of bipartite
cuts and nevertheless exhibit genuine multipartite entanglement. Finally, we
show that every $k$-positive but not completely positive map is associated to a
family of nondecomposable maps.
