  I show that the cluster LX-sigma relation should be sensitive to cosmologies
with a scale-free power spectrum of initial density fluctuations, P(k) ~ k^n. I
derive the dependence, and argue that a conservative interpretation of current
observations implies n < -2.0 and n < -1.1 at the one-sided 90% and 99%
confidence levels, respectively. This result, which agrees with constraints on
n from the x-ray cluster temperature function, should be roughly independent of
the value of Omega or Lambda.
