  The interplay between magic number stabilities and superfluidity of small
para-hydrogen clusters with sizes $N = 5$ to 40 and temperatures $0.5 K \leq T
\leq 4.5 $K is explored with classical and quantum Path Integral Monte Carlo
calculations. Clusters with $N < 26$ and T $\leq 1.5 K$ have large superfluid
fractions even at the stable magic numbers 13, 19, and 23. In larger clusters,
superfluidity is quenched especially at the magic numbers 23, 26, 29, 32, and
37 while below 1 K, superfluidity is recovered for the pairs $(27,28)$,
$(30,31)$, and $(35,36)$. For all clusters superfluidity is localized at the
surface and correlates with long exchange cycles involving loosely bound
surface molecules.
