  Almost all massive stars are part of a binary system. Given the wide range of
separations at which these companions are found, several observational
techniques have been adopted to characterize them, but contrasts greater than 4
in the H-band have never been reached between 0".1 and 1". We used VLT/SPHERE
to observe simultaneously with the IRDIS and IFS sub-systems 18 O-type stars
within 6 kpc and ages between 1-5 Myrs to probe the existence of stellar
companions in the angular separation range from 0".15 to 6" down to very low
mass ratios. The IFS YJH- band observations have allowed us to probe the
presence of sub-solar companions in a 1".7x1".7 field-of-view down to magnitude
limits of deltaH=10 at 0".4. In the wider 12"x12" IRDIS field-of-view, we
reached contrasts of deltaK=12 at 1", enabling us to look for even fainter
companions. This paper presents five newly discovered intermediate (<1")
separation companions, three of which are smaller than 0.2M_sun. If confirmed
by future analyses of proper motions, these new detections represent the
lowest-mass companions ever found around O-type stars. Assuming that all
sources detected within 1" are physically bound, the observed fraction of
companions for O-type stars between 0".15 and 0".9 is 0.39+/-0.15, whereas it
increases to 1.6+/-0.3 in the separation range from 0".9 to 6". These findings
clearly support the notion that massive stars form almost exclusively in
multiple systems, and that larger AO-assisted coronagraphic surveys are crucial
in placing constraints on the multiplicity properties of massive star
companions in regions of the parameter space that have previously gone
unexplored, and demonstrate that the companion mass function is populated down
to the lowest stellar masses.
