Contrapositive and Contradiction · Superchallenge problem

Fermat’s test is used by contrapositive: if $p$ is prime then $p \mid 2^p - 2$, so if $n \nmid 2^n - 2$ then $n$ is composite. The test can fail to detect a composite. What is the smallest composite $n$ with $n \mid 2^n - 2$?