We investigate the mass function in the substellar domain down to a few Jupiter masses in the young sigma Orionis open cluster (3+/-2 Ma, d = 360^+70_-60 pc). We have performed a deep IJ-band search, covering an area of 790 arcmin^2 close to the cluster centre. This survey was complemented with an infrared follow-up in the HKs- and Spitzer 3.6-8.0 mum-bands. Using colour-magnitude diagrams, we have selected 49 candidate cluster members in the magnitude interval 16.1 mag < I < 23.0 mag. Accounting for flux excesses at 8.0 mum and previously known spectral features of youth, 30 objects are bona fide cluster members. Four are first identified from our optical-near infrared data. Eleven have most probable masses below the deuterium burning limit and are classified as planetary-mass object candidates. The slope of the substellar mass spectrum (Delta N / Delta M = a M^-alpha) in the mass interval 0.11 Msol M < 0.006 Msol is alpha = +0.6+/-0.2. Any opacity mass-limit, if these objects form via fragmentation, may lie below 0.006 Msol. The frequency of sigma Orionis brown dwarfs with circumsubstellar discs is 47+/-15 %. The continuity in the mass function and in the frequency of discs suggests that very low-mass stars and substellar objects, even below the deuterium-burning mass limit, may share the same formation mechanism.
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