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We present relative astrometric and photometric measurements of visual double stars made in 2013–2015, with PISCO2 installed at the 76‐cm refractor of Côte d'Azur Observatory in Nice (France). Our observing list contains orbital couples as well as double stars whose motion is still uncertain. Most of the observations were done in 2015, but some other observations of wide couples were done in 2013–2014 (0.3% of the total of the observations). Three different techniques were used for obtaining measurements: lucky imaging, speckle interferometry and the direct vector autocorrelation method. From our observations of 2837 multiple stars, we obtained 5182 new measurements with angular separations in the range of 0″$$ {}^{{\prime\prime} } $$.1–32″$$ {}^{{\prime\prime} } $$ and an average accuracy of 0″.018$$ {0}^{{\prime\prime} }.018 $$. The mean error on the position angles is 0°.8. Most of the position angles were determined without the usual 180° ambiguity with the application of the direct vector autocorrelation technique and/or by inspection of the Lucky images or the long integration files. We managed to routinely monitor faint systems (mV≈9−11$$ {m}_V\approx 9-11 $$) with large magnitude difference (up to ΔmV≈4.5$$ \Delta {m}_V\approx 4.5 $$). We have thus been able to measure 21 systems containing red dwarf stars that had been poorly monitored since their discovery, from which we estimated the stellar masses thanks to Gaia measurements. We also measured the magnitude difference of the two components of 1079 double stars with an estimated error of 0.2 mag. Except for a few objects that are discussed, our measurements are in good agreement with the ephemerides computed with published orbital elements, even for the double stars whose separation is smaller than the diffraction limit. Thanks to good seeing images and with the use of high‐contrast numerical filters, we have also been able to obtain 196 measurements with an angular separation smaller than the diffraction limit of our instrumentation, and consistent with those obtained with larger telescopes. We also report measurements of the 164 new double stars that we found in the files obtained during the observations. Finally, from a study of the DR3 Gaia release, it is shown that all the objects of the Tycho Double Star Catalog that we did not resolve in 2015 are probably false detections by Tycho. [ABSTRACT FROM AUTHOR]