Given a positive integer $n$ , an integer $0 < m < n$ is a totative of $n$ if $\gcd(m, n) = 1$ . Put another way, all the smaller integers than $n$ that are coprime to $n$ are totatives of $n$ .

For example, the totatives of 21 are 1, 2, 4, 5, 8, 10, 11, 13, 16, 17, 19 and 20.

The count of totatives of $n$ is Euler's totient function $\phi(n)$ . The set of totatives of $n$ forms a reduced residue system modulo $n$ . The word ``totative'' was coined by James Joseph Sylvester, who also coined ``totient'' (though despite occasional usage in some papers and books, the term ``totative'' has not caught on the way ``totient'' has).