Context. Stellar physical properties of star clusters are poorly known. Aims. Our goals are to perform a spectrophotometric study of the B star population in open clusters to derive accurate stellar parameters, search for the presence of circumstellar envelopes, and discuss the characteristics of these stars. Methods. The BCD spectrophotometric system is a powerful tool to obtain fundamental parameters and infer the main properties of open clusters: distance modulus, color excess, and age. We inspected the Balmer discontinuity to seek circumstellar disks and identify Be-star candidates. High resolution spectra in the H$alpha$ region are used to confirm the Be nature. Results. We provide Teff , log g, Mv , Mbol and spectral types for a sample of 68 stars in the field of the open clusters NGC 6087, NGC 6250, NGC 6383, and NGC 6530, as well as the cluster distances, ages and reddening. Then, based on a sample of 230 B stars in the direction of the 11 open clusters studied along this series of three papers, we report 6 new Be stars, 4 blue straggler candidates, and 15 B-type stars (called Bdd) with a double Balmer discontinuity. We also find that the majority of the Be stars are dwarfs and present a maximum at the spectral type B2-B4 in young and intermediate-age open clusters. Another maximum of Be stars is observed at the spectral type B6-B8 in open clusters older than 40 Myr, where the population of Bdd stars also becomes relevant. Conclusions. Our results support previous statements that the Be phenomenon is present along the whole main sequence band and occurs in very different evolutionary states. We find clear evidence of an increase of stars with circumstellar envelopes with cluster age. The Be phenomenon reaches its maximum in clusters of intermediate age and the number of B stars with circumstellar envelopes (Be+Bdd stars) is also high for the older clusters.
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