The AJ-conjecture and cabled knots over torus knots
  We show that most cabled knots over torus knots in $S^3$ satisfy the AJ-conjecture, namely each $(r,s)$-cabled knot over each $(p,q)$-torus knot satisfies the $AJ$-conjecture if $r$ is not a number between $0$ and $pqs$. 
Dennis Ruppe and Xingru Zhang
math.GT