Definition: DivisorClosed Sets
A divisorclosed subset \(\mathcal N\subseteq \mathbb Z\) of integers is a set, which with every $n\in \mathcal N$ contains also all divisors \(d\mid n\) of $n.$
Examples
 $\mathcal N=\mathbb Z$ is divisorclosed.
 $\mathcal N=\{\pm 1\}\cup \{n\in \mathbb Z:n=6k\pm 1,k\in\mathbb Z\}$ is divisorclosed.
 The set of all even numbers is not divisor closed, since it would contain $1$, and $1$ is not even.
Mentioned in:
Lemmas: 1
Proofs: 2
Thank you to the contributors under CC BYSA 4.0!
 Github:
