We compute the principal contribution to the index in the supersymmetric qu
antum mechanical systems which are obtained by reduction to 0 + 1 dimension
s of N = 1, D = 4, 6, 10 super-Yang-Mills theories with gauge group SU(N).
The results are: 1/N-2 for D = 4, 6, Sigma(d/N) 1/d(2) for D = 10. We also
discuss the D = 3 case.