  Star formation in massive galaxies is quenched at some point during
hierarchical mass assembly. To understand where and when the quenching
processes takes place, we study the evolution of the total star formation rate
per unit total halo mass (\Sigma(SFR/M)) in three different mass scales: low
mass halos (field galaxies), groups, and clusters, up to a redshift ~1.6. We
use deep far-infrared PACS data at 100 and 160 um to accurately estimate the
total star formation rate of the Luminous Infrared Galaxy population of 9
clusters with mass ~10^{15} M_{\odot}, and 9 groups/poor clusters with mass ~ 5
x 10^{13} M_{\odot}. Estimates of the field \Sigma(SFR/M) are derived from the
literature, by dividing the star formation rate density by the mean comoving
matter density of the universe. The field \Sigma(SFR/M) increases with redshift
up to z~1 and it is constant thereafter. The evolution of the \Sigma(SFR/M)-z
relation in galaxy systems is much faster than in the field. Up to redshift
z~0.2, the field has a higher \Sigma(SFR/M) than galaxy groups and galaxy
clusters. At higher redshifts, galaxy groups and the field have similar
\Sigma(SFR/M), while massive clusters have significantly lower \Sigma(SFR/M)
than both groups and the field. There is a hint of a reversal of the SFR
activity vs. environment at z~1.6, where the group \Sigma(SFR/M) lies above the
field \Sigma(SFR/M)-z relation. We discuss possible interpretations of our
results in terms of the processes of downsizing, and star-formation quenching.
