Context : The very young \sigma Orionis cluster ( \sim 3 Ma ) is a cornerstone for the understanding of the formation of stars and substellar objects down to planetary masses . However , its stellar population is far to be completely known . Aims : This study has the purpose of identyfing and characterising the most massive stars of \sigma Orionis to complement current and future deep searches for brown dwarfs and planetary-mass objects in the cluster . Methods : I have cross-correlated the sources in the Tycho and 2MASS catalogues in a region of 30 arcmin radius with centre in the O-type star \sigma Ori A . In the area , I have studied the membership in the Ori OB 1b Association of the brightest stars in the optical using astrometric , X-ray and infrared and optical photometric data from public catalogues and spectroscopic data from the literature . Results : A list of 26 young stars , four candidate young stars and 16 probable foreground stars has arised from the study . Seven young stars probably harbour discs ( four are new ) . There is no mass-dependence of the disc frequency in the cluster . I have derived for the first time the mass spectrum in \sigma Orionis from 1.1 to 24 M _ { \odot } ( \alpha = +2.0 ^ { +0.2 } _ { -0.1 } ; roughly Salpeter-like ) . I have also provided additional proofs on the existence of several spatially superimposed stellar populations in the direction of \sigma Orionis . Finally , the cluster may be closer and older than previously considered Tables 13 and 14 are only available in electronic form at the CDS via anonymous ftp to cdsarc.u-strasbg.fr ( 130.79.128.5 ) or via http : //cdsweb.u-strasbg.fr/cgi-bin/qcat ? J/A+A/ . . Conclusions :