  In this work we investigate small clusters of helium atoms using the
hyperspherical harmonic basis. We consider systems with $A=2,3,4,5,6$ atoms
with an inter-particle potential which does not present a strong repulsion at
short distances. We use an attractive gaussian potential that reproduces the
values of the dimer binding energy, the atom-atom scattering length, and the
effective range obtained with one of the widely used He-He interactions, the
LM2M2 potential. In systems with more than two atoms we consider a repulsive
three-body force that, by construction, reproduces the trimer binding energy of
the LM2M2 potential. With this model, consisting in the sum of a two- and
three-body potential, we have calculated the spectrum of clusters formed by
four, five and six helium atoms. We have found that these systems present two
bound states, one deep and one shallow close to the threshold fixed by the
energy of the $(A-1)$-atom system. Universal relations between the energies of
the excited state of the $A$-atom system and the ground state energy of the
$(A-1)$-atom system are extracted as well as the ratio between the ground state
of the $A$-atom system and the ground state energy of the trimer.
