  The NA60 experiment has studied low-mass muon pair production in
proton-nucleus collisions with a system of Be, Cu, In, W, Pb and U targets,
using a 400 GeV proton beam at the CERN SPS. The transverse momentum spectra of
the $\rho/\omega$ and $\phi$ mesons are measured in the full $p_\mathrm{T}$
range accessible, from $p_\mathrm{T} = 0$ up to 2 GeV/$c$. The nuclear
dependence of the production cross sections of the $\eta$, $\omega$ and $\phi$
mesons has been found to be consistent with the power law $\sigma_\mathrm{pA}
\propto \mathrm{A}^\alpha$, with the $\alpha$ parameter increasing as a
function of $p_\mathrm{T}$ for all the particles, and an approximate hierarchy
$\alpha_\eta \approx \alpha_\phi > \alpha_\omega$. The cross section ratios
$\sigma_\eta/\sigma_\omega$, $\sigma_\rho/\sigma_\omega$ and
$\sigma_\phi/\sigma_\omega$ have been studied as a function of the size A of
the production target, and an increase of the $\eta$ and $\phi$ yields relative
to the $\omega$ is observed from p-Be to p-U collisions.
