I'd like to suggest reopening http://mathoverflow.net/questions/253250/covering-systems. As I wrote in a comment, 

Why is this closed? Covering systems are a recognized area of research in Number Theory. It's known that in an irredundant cover with a modulus divisible by a prime $p$
 there are at least $p$
 moduli divisible by $p$. This asks whether, if there is a modulus divisible by a power of a prime $p$, there are at least $p$
 moduli divisible by that power of $p$. Seems like a reasonable research question to me. 

[Also, I think I can answer it.]