For example, the Carmichael numbers (it is now known there are infinitely many).

Stronger version:........

This has been posted before see http://artofproblemsolving.com/community/c6h1073751p4682624

$n=\frac{9^{p}-4^p}{5}$ for large $p\in P$.

$n=3^{2^k}-2^{2^k}$