  We calculate the maximum mass of neutron stars for three different equations
of state (EOS) based on generalized Skyrme functionals that are simultaneously
fitted to essentially all the 2003 nuclear mass data (the rms deviation is 0.58
MeV in all three cases) and to one or other of three different equations of
state of pure neutron matter, each determined by a different many-body
calculation using realistic two- and three-body interactions but leading to
significantly different degrees of stiffness at the high densities prevailing
in neutron-star interiors. The observation of a neutron star with mass 1.97
$\pm$ 0.04 $\mathcal{M}_{\odot}$ eliminates the softest of our models (BSk19),
but does not discriminate between BSk20 and BSk21. However, nuclear-mass
measurements that have been made since our models were constructed strongly
favor BSk21, our stiffest functional.
