Re: is there a name for these sets?

If gcd(n, x) = k then gcd(n/k, x/k) = 1, so S(n, k) = k S(n/k, 1). The
set S(m, 1) is called the set of totatives of m, so you could call this
set "the k-th multiples of the totatives of n/k," or something similar.
Actually, you can probably restate whatever you're using this set for
in terms of totatives.

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