While solving number theory problems I sometimes I have to use a function that can be defined as
$$ f(n) = \begin{cases} 1 & \text{ if } n = 1, \\ 0 & \text{ if } n > 1. \end{cases} $$
where $ n $ is a positive integer.
For example, using this function, we can define Euler's totient function as
$$ \varphi(n) = \sum_{k=1}^n f(\gcd(k, n))$$
where $ n $ is a positive integer.
Is there a name or notation for such a function already? I just want to make sure that I do not create my own notation for something that already has a popular name or notation in mathematics.