Context: The very young sigma Orionis cluster (about 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

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... 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 Msol (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.