It's a straightforward rip-off this problem from PCMI:
The sum of 4's divisors are 7. The sum of 5's divisors are 6. Etc.
Except that a lot of cool stuff happens along the way. I don't want to dish out any spoilers, but there is a lot of cool stuff to dig into.
We're talking about divisors, summing and multiplication here, so it's a good workout for the elementary school brain. There are also ample opportunities for spotting patterns, and a few good chances to offer justifications. It's a ton of fun when it works.
The only thing you need to work around is function notation, but that's not a big deal.
Anyway, I do love this problem, and until you dig into the math you're just going to have to trust me that it has connections with exponents, adding fractions, .9999... = 1 and all sorts of other rich elementary school (and high school and number theory) topics. It's absolutely and truly one of my favorite functions and problems.
Only issue: it was definitely not a hit on the first day of class with my 4th graders. They struggled with finding divisors and their multiplication isn't strong enough to make the sorts of connections that make this a blast. It was OK, and there were a few cool moments when I pointed some things out, but overall it was a bit disappointing.
But that's more an issue with my taking an unnecessary risk on the first day than with the actual problem. I imagine that I'll bring this back into class once the kids are up to snuff, operations-wise. Good practice for all sorts of operations, and a lot of patterns to sniff out too.
Let's hang out a bit in the comments. I'll give you two prompts: (1) Would this work with your elementary school students? Why, why not, etc. (2) Can you think of more "higher" math topics that would do well in a small-person classroom?