# Can be written as $$\frac{A}{B}$$, where $$A$$ and $$B$$ are not coprime?!

The sum of the reciprocals of all numbers that have a prime factorization of $$A^m B^n$$, where $$m$$ and $$n$$ are positive integers and $$A$$ and $$B$$ are positive integers that are not necessarily coprime can be expressed as $$\dfrac{A}{B}$$. What is $$A+B$$?

Inspiration: Mind your 3's and 2's.

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