  We prove a Cwikel-Lieb-Rozenblum type inequality for the number of negative
eigenvalues of the Hardy-Schr\"odinger operator $-\Delta - (d-2)^2/(4|x|^2)
-W(x)$ on $L^2(\mathbb{R}^d)$. The bound is given in terms of a weighted
$L^{d/2}-$norm of $W$ which is sharp in both large and small coupling regimes.
We also obtain a similar bound for the fractional Laplacian.
