  The radiative type-I seesaw has been already implemented to explain the
lightness of Majorana neutrinos with both Majorana and Dirac heavy fermions,
and the lightness of Dirac neutrinos with Dirac heavy fermions. In this work we
present a minimal implementation of the radiative type-I seesaw with light
Dirac neutrinos and heavy Majorana fermions. An inert doublet and a complex
singlet scalar complete the dark sector which is protected by an Abelian
fermiophobic gauge symmetry that also forbids tree level mass contributions for
the full set of light neutrinos. A fermion vector-like extension of the model
is also proposed where the light right-handed neutrinos can thermalize in the
primordial plasma and the extra gauge boson can be directly produced at
colliders. In particular, the current upper bound on $\Delta N_{\text{eff}}$
reported by PLANCK points to large ratios $M_{Z'}/g'\gtrsim 40\ \text{TeV}$
which can be competitive with collider constraint for $g'$ sufficiently large
in the ballpark of the Standard Model values, while future cosmic microwave
background experiments may probe all the no minimal models presented here.
