# GCD generator

Number Theory Level pending

Let $$R$$ be a subset of $$\mathbb N \times \mathbb N$$ defined as follows:

$$R= \{ (a,b) \in \mathbb N \times \mathbb N: b$$ is the lowest natural number with $$\gcd(b+1, 2b+1)=a\}$$.

For each $$(a,b)$$, let $$A$$ denote $$(a+b)$$. What is sum of all possible values of $$A$$?

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