  We show that a recently conjectured form for perturbative supersymmetric
partition functions on spheres of general dimension $d$ is consistent with the
flat space limit of 6-dimensional $\mathcal{N}=1$ super Yang-Mills. We also
show that the partition functions for $\mathcal{N}=1$ 8- and 9-dimensional
theories are consistent with their known flat space limits.
