  We compute the principal contribution to the index in the supersymmetric
quantum mechanical systems which are obtained by reduction to 0+1 dimensions of
$\mathcal{N}=1$, $D=4,6,10$ super-Yang-Mills theories with gauge group SU(N).
The results are: ${1\over{N^{2}}}$ for $D=4,6$, $\sum_{d | N} {1\over{d^{2}}}$
for D=10. We also discuss the D=3 case.
