  We study the effects of the addition of the charm quark on the QCD equation
of state at zero and nonzero chemical potential on lattices with $N_t=6$. Our
ensembles are quenched with respect to charm and the charm quark is a valence
staggered quark. Along the trajectory of constant physics the ratio $m_s/m_c$
is kept constant after tuning the charm quark mass at a lattice spacing of
about 0.09 fm. We find that the charm quark has a significant contribution to
the equation of state at zero chemical potential already at temperatures
between about $1.2T_c$ and $2T_c$. The additional contribution at nonzero
chemical potential vanishes within the current statistical uncertainty.
