How do you refer to those sequences $\{a_{n}\}_{n \in \mathbb{Z}^{+}}$ of integers that satisfy the condition $\text{gcd}(a_{m}, a_{n}) = a_{\text{gcd}(m,n)}$ for every $(m,n) \in \mathbb{Z}^{+} \times \mathbb{Z}^{+}$?

I believe some authors refer to 'em as "Mersenne sequences". Is this the most established term for integer sequences of that type?

Thanks in advance for your replies.