  In this work we extend the discussion that was began in the Ref. [A. L. de
Paula Jr., J. G. G. de Oliveira Jr., J. G. Peixoto de Faria, Dagoberto S.
Freitas and M. C. Nemes, {\it Phys. Rev.} {\bf A89}, (2014) 022303] to deal
with the dynamics of the concurrence of a many-body system. In that previous
paper, the discussion was focused in the residual entanglement between the
partitions of the system. The purpose of the present contribution is to shed
some light on the dynamical properties of entanglement among the environment
oscillators. We consider a system consisting of a harmonic oscillator linearly
coupled to N others and solve the corresponding dynamical problem analytically.
We divide the environment in arbitrary two partitions and the entanglement
dynamics between any of these partitions is quantified and it shows that in the
case that excitations in each partitions are equal, the concurrence reaches the
value one and the two partition of the environment are maximally entangled. For
long times the excitations of the main oscillator are completely transferred to
environment and the environment oscillators are found entangled.
