  Two new families of completely integrable perturbations of the N-dimensional
isotropic harmonic oscillator Hamiltonian are presented. Such perturbations
depend on arbitrary functions and N free parameters and their integrals of
motion are explicitly constructed by making use of an underlying h_6-coalgebra
symmetry. Several known integrable Hamiltonians in low dimensions are obtained
as particular specializations of the general results here presented. An
alternative route for the integrability of all these systems is provided by a
suitable canonical transformation which, in turn, opens the possibility of
adding (N-1) `Rosochatius' terms that preserve the complete integrability of
all these models.
