Find the rule

The rule is very simple but insanely hard to figure out. You need to think outside the box.

Hint:
(1,2,3) is non-acceptable.

Yeah, you are correct 🐱-👤

Try to solve mine meow...

4,8,6

(4,8,6) is non-acceptable.

Hint:
Property 2: If (a,b,c) is non-acceptable, k is a rational number, ka, kb, kc are integers, so is (ka,kb,kc) non-acceptable.

Examples of the properties.
Prove that (2,3,4) is non-acceptable.
Proof: since (4,8,6) is non-acceptable, (2,4,3) is non-acceptable due to Property 2. Use property 1 we can deduce that (2,3,4) is non-acceptable.

To further simplify the problem, you guys can also propose some properties about my rule and I will answer whether they hold or not. If not I will give a counterexample.

So I can't use the numbers 1,2,3,4,6 and 8?