  We perform a perturbative calculation of the influence of dynamical HISQ
fermions on the perturbative improvement of the gluonic action in the same way
as we have previously done for asqtad fermions. We find the fermionic
contributions to the radiative corrections in the Luescher-Weisz gauge action
to be somewhat larger for HISQ fermions than for asqtad. Using one-loop
perturbation theory as a test, we estimate that omission of the fermion-induced
radiative corrections in dynamical asqtad simulations will give a measurable
effect. The one-loop result gives a systematic shift of about -0.6% in (r_1/a)
on the coarsest asqtad improved staggered ensembles. This is the correct sign
and magnitude to explain the scaling violations seen in Phi_B on dynamical
lattice ensembles.
