  Using data from the Gaia Data Release 3 (Gaia DR3) and Kepler/K2, we present
a catalog of 16 open clusters with ages ranging from 4 to 4000 Myr, which
provides detailed information on membership, binary systems, and rotation. We
assess the memberships in 5D phase space, and estimate the basic parameters of
each cluster. Among the 20,160 members, there are 4,381 stars identified as
binary candidates and 49 stars as blue straggler stars. The fraction of
binaries vary in each cluster, and the range between 9% to 44%. We obtain the
rotation periods of 5,467 members, of which 4,304 are determined in this work.
To establish a benchmark for the rotation-age-color relation, we construct
color-period diagrams. We find that the rotational features of binaries are
similar to that of single stars, while features for binaries are more scattered
in the rotation period. Moreover, the morphology of the color-period
relationship is already established for Upper Scorpius at the age of 19 Myr,
and some stars of varying spectral types (i.e. FG-, K-, and M-type) show
different spin-down rates after the age of ~110 Myr. By incorporating the
effects of stalled spin-down into our analysis, we develop an empirical
rotation-age-color relation, which is valid with ages between 700 - 4000 Myr
and colors corresponding to a range of 0.5 < (G_BP-G_RP)0 < 2.5 mag.
