# 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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