  We explore the dependence of the subhalo mass function on the spectral index
n of the linear matter power spectrum using scale-free Einstein-de Sitter
simulations with n=-1 and n=-2.5. We carefully consider finite volume effects
that may call into question previous simulations of n<-2 power spectra.
Subhaloes are found using a 6D friends-of-friends algorithm in all haloes
originating from high-sigma peaks. For n=-1, we find that the cumulative
subhalo mass function is independent of the parameters used in the subhalo
finding algorithm and is consistent with the subhalo mass function found in
LCDM simulations. In particular, the subhalo mass function is well fit by a
power-law with an index of alpha=-0.9, that is the mass function has roughly
equal mass in subhaloes per logarithmic interval in subhalo mass. Conversely,
for n=-2.5, the algorithm parameters affect the subhalo mass function since
subhaloes are more triaxial with less well defined boundaries. We find that the
index alpha is generally larger with alpha>=-0.75. We infer that although the
subhalo mass function appears to be independent of n so long as n>=-2, it
begins to flatten as n->-3. Thus, the common practice of using alpha=-1.0 may
greatly overestimate the number of subhaloes at the smallest scales in the CDM
hierarchy.
