Jordan's totient function

Let ${\displaystyle k}$ be a positive integer. In number theory, Jordan's totient function ${\displaystyle J_{k}(n)}$ of a positive integer ${\displaystyle n}$ is the number of ${\displaystyle k}$-tuples of positive integers all less than or equal to ${\displaystyle n}$ that form a coprime ${\displaystyle (k+1)}$-tuple together with ${\displaystyle n}$. This is a generalisation of Euler's totient function, which is ${\displaystyle J_{1}}$. The function is named after Camille Jordan.

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