Jordan's totient function ( $J_{k} (n)$ )

The Jordan totient function counts ordered

k

n

that together with

n

have greatest common divisor one. The inclusion-exclusion principle gives

J_{k} (n) = n^{k} \prod_{p ∣ n} (1 - p^{- k}) .

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Jordan's totient function, denoted as \( J_k(n) \), is a generalization of Euler's totient function.

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