For the positive integer $n$, let $⟨n⟩$ denote the sum of all the positive divisors of $n$ with the exception of itself. For example, $⟨4⟩=1+2=3$ and $⟨12⟩=1+2+3+4+6=16$. What is $⟨⟨⟨10⟩⟩⟩$?