Determination of the number of $\psi (3686)$ events taken at BESIII

The number of $\psi (3686)$ events collected by the BESIII detector during the 2021 run period is determined to be $(2259.3\pm 11.1)\times {10}^6$ by counting inclusive $\psi (3686)$ hadronic events. The uncertainty is systematic and the statistical uncertainty is negligible. Meanwhile, the numbers of $\psi (3686)$ events collected during the 2009 and 2012 run periods are updated to be $(107.7\pm 0.6)\times {10}^6$ and $(345.4\pm 2.6)\times {10}^6$, respectively. Both numbers are consistent with the previous measurements within one standard deviation. The total number of $\psi (3686)$ events in the three data samples is $(2712.4\pm 14.3)\times {10}^6$.