The initial luminosity and mass functions of the Galactic open clusters

(... abridged) The observed luminosity function can be constructed in a range of absolute integrated magnitudes $I_{M_V}= [-10, -0.5]$ mag, i.e. about 5 magnitudes deeper than in the most nearby galaxies. It increases linearly from the brightest limit to a turnover at about $I_{M_V}\approx-2.5$. The slope of this linear portion is $a=0.41\pm0.01$, which agrees perfectly with the slope deduced for star cluster observations in nearby galaxies. (...) We find that the initial mass function of open clusters (CIMF) has a two-segment structure with the slopes $\alpha=1.66\pm0.14$ in the range $\log M_c/M_\odot=3.37...4.93$ and $\alpha=0.82\pm0.14$ in the range $\log M_c/M_\odot=1.7...3.37$. The average mass of open clusters at birth is $4.5\cdot 10^3 M_\odot$, which should be compared to the average observed mass of about $700 M_\odot$. The average cluster formation rate derived from the comparison of initial and observed mass functions is $\bar{\upsilon}=0.4 \mathrm{kpc}^{-2}\mathrm{Myr}^{-1}$. Multiplying by the age of the Galactic disc (T = 13 Gyr) the predicted surface density of Galactic disc field stars originating from dissolved open clusters amounts to $22 M_\odot \mathrm{pc}^{-2}$ which is about 40% of the total surface density of the Galactic disc in the solar neighbourhood. Thus, we conclude that almost half of all field stars were born in open clusters, a much higher fraction than previously thought.