  We combine results from imaging searches for substellar objects in the sigma
Orionis cluster and follow-up photometric and spectroscopic observations to
derive a census of the brown dwarf population in a region of 847 arcmin^2. We
identify 64 very low-mass cluster member candidates in this region. We have
available three color (IZJ) photometry for all of them, spectra for 9 objects,
and K photometry for 27% of our sample. These data provide a well defined
sequence in the I vs I-J, I-K color magnitude diagrams, and indicate that the
cluster is affected by little reddening despite its young age (~5 Myr). Using
state-of-the-art evolutionary models, we derive a mass function from the
low-mass stars (0.2 Msol) across the complete brown dwarf domain (0.075 Msol to
0.013 Msol), and into the realm of free-floating planetary-mass objects (<0.013
Msol). We find that the mass spectrum (dN/dm ~ m^{-alpha}) increases toward
lower masses with an exponent alpha = 0.8+/-0.4. Our results suggest that
planetary-mass isolated objects could be as common as brown dwarfs; both kinds
of objects together would be as numerous as stars in the cluster. If the
distribution of stellar and substellar masses in sigma Orionis is
representative of the Galactic disk, older and much lower luminosity
free-floating planetary-mass objects with masses down to about 0.005 Msol
should be abundant in the solar vicinity, with a density similar to M-type
stars.
