I can't convincingly argue that it's incorrect, but I wouldn't use it. I understand you want to ask a question to which the correct answer is
"Monday, Tuesday, Wednesday, Thursday, Friday, Saturday and Sunday."
In this case, I would think about week as a unique object: a unit of time consisting of unique "days": Monday, Tuesday, etc.
However, I would say
How many centimeters are there in a meter?
I'm not sure why. The difference seems to be that the parts of a meter (the centimeters) are not thought to be uniquely determined -- no one (I think) thinks about the first and the fifty-second centimeter of a meter, though it's possible. I don't quite see however how it explains the indefinite article.