  Harmonic oscillators with a centrifugal spike are analysed, via a
non-Hermitian regularization, within a complexified SUSY quantum mechanics. The
formalism enables us to construct the factorized creation and annihilation
operators. We show how the real though, generically, non-equidistant spectrum
complies with the current SUSY-type isospectrality and degeneracy in an unusual
way.
