Suppose that $n$ is a fixed integer different from zero,
$D$ is the set of divisors of $n$;
$D=\{1,d_1,...,n\}.$
For every $d_i$ belongs to D, We introduce the set:
$S^n(d_i)=\{1 \leq s \leq n; gcd(s,n)=d_i\}.$
The question is:
Is there any formula to find the cardinal of $S(d_i)$?