Hi all. There is a conjecture by Erdős that states "There doesn't exist an integer covering system with all moduli odd AND distinct." The link is http://en.wikipedia.org/wiki/Covering_system

I think that, if a covering exists with all moduli distinct, not only the lcm of the moduli must be even, it must also be abundant. In this sense, the odd perfect number conjecture and this conjecture are related in my opinion.

Is my conjecture true or any counterexample exists? Has the same conjecture been made before? Any help would be appreciated. Thanks in advance.