  We present the sharpest and deepest near infrared photometric analysis of the
core of R136, a newly formed massive star cluster at the centre of the 30
Doradus star forming region in the Large Magellanic Cloud. We used the extreme
adaptive optics of the SPHERE focal instrument implemented on the ESO Very
Large Telescope and operated in its IRDIS imaging mode, for the second time
with longer exposure time in the H- and K filters. Our aim was to (i) increase
the number of resolved sources in the core of R136, and (ii) to compare with
the first epoch to classify the properties of the detected common sources
between the two epochs. Within the field of view (FOV) of 10.8"x12.1" (2.7pc
x3.0pc), we detected 1499 sources in both H and K filters, for which 76% of
these sources have visual companions closer than 0.2". The larger number of
detected sources, enabled us to better sample the mass function (MF). The MF
slopes are estimated at ages of 1, 1.5 and 2 Myr, at different radii, and for
different mass ranges. The MF slopes for the mass range of 10-300 solar-mass
are about 0.3 dex steeper than the mass range of 3-300 solar-mass, for the
whole FOV and different radii. Comparing the JHK colours of 790 sources common
in between the two epochs, 67% of detected sources in the outer region (r >3")
are not consistent with evolutionary models at 1-2 Myr and with extinctions
similar to the average cluster value, suggesting an origin from ongoing star
formation within 30 Doradus, unrelated to R136.
