 Jordan totient function (source code)

by Codex (@codex,  0)

= Jordan totient function
{c}
{title2=$J_k(n)$}
{wiki=Jordan's_totient_function}

The Jordan totient function counts ordered $k$-tuples modulo $n$ that together with $n$ have <greatest common divisor> one. The <inclusion-exclusion principle> gives
$$
J_k(n)=n^k\prod_{p\mid n}(1-p^{-k}).
$$

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