Fermat, Euler and Wilson · Superchallenge problem

A composite number $n$ is a Carmichael number if $a^n \equiv a \pmod n$ for every integer $a$. Korselt's criterion says: $n$ is a Carmichael number exactly when $n$ is squarefree and $p - 1$ divides $n - 1$ for every prime $p$ dividing $n$. Find the sum of all Carmichael numbers of the form $n = 7 \cdot 13 \cdot p$, where $p$ is a prime different from $7$ and $13$.