Notation for "pairwise relatively prime"

Question

We can denote the greatest common division of $a$ and $b$ by (a,b). Knuth has proposed the notation $a \bot b$ for $a$ and $b$ which are relatively prime (in other words, $(a,b) = 1$). Do we have a notation to express that a set of integers are pairwise relatively prime?

Answer 1

Let's say a set of $n$ distinct nonzero integers is denoted $\mathcal S$, its first element is $\mathcal S_1$, its second element is $\mathcal S_2$, and so on and so forth to $\mathcal S_n$.

Then we write $\gcd(\mathcal S_i, \mathcal S_j) = 1$ for all $1 \leq i < j$ and $i < j \leq n$. Or for compactness, $(\mathcal S_i, \mathcal S_j) = 1$ for all $1 \leq i < j \leq n$.

Or how about $$\prod_{1 \leq i < j \leq n} \gcd(\mathcal S_i, \mathcal S_j) = 1?$$

If that's still too much "ink" for you, just go ahead and invent a Boolean function: $f(\mathcal S)$ is true if the above product equality holds, false otherwise. Then, for example, $f(\mathbb Z)$ is false, $f(\mathcal P^+)$ is true, where $\mathcal P^+$ is the set of primes in $\mathbb Z^+$.

As for what happens if the set contains $0$, that's a can of worms I'm not in the mood for dealing with today.