The model number is 113.179255.
A picture of the filter is here:
The nut you see at the top of the picture won't budge. Thus, I cannot remove the filter. I called Sears and they said it should come off easily without any tools. The vacuum is less than a year old and only used a couple of times. I don't think I ever removed the filter before. You can see how mangled that plastic nut is now after trying every tool the in drawer to remove it. (Why would they use a plastic nut?) I must be missing something really obvious. One other thing I should mention, the owners manual shows the parts blow up which includes a "filter nut lever." I didn't see anything like that attached to or near the nut.
Thanks for your replies.