Euler's totient function

Euler's totient function counts the totatives of a given integer $n$, i.e. the positive integers up to $n$ that are coprime to $n$.

It is specified $\phi (n)$, giving its alternate name, "Euler's phi function"

In other words, it is the number of integers $k$ in the range $1\le k\le n$ for which the greatest common divisor $gcd(n,k)$ is equal to 1.

Euler's theorem
Euler's totient function is multiplicative for coprime values.

See also

• Euler's product formula