Equation Involving GCD

Find the sum of all distinct \(a \in \mathbb{N}\) for which there exists a positive integer \(b\) such that \[a+b^2 + \left( \gcd (a,b) \right) ^3 = ab \cdot \gcd (a,b).\]

Details and assumptions

  • \(a,b\) are both positive.
  • This problem is not original.
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