Attribution of Numbers 2020 is an “undulating” as well as “abundant” number. Hope the year 2020 throws your life on an undulating path that ultimately leads to abundance ( Happy New Year) . My question revolves more around the attribution of numbers with sometimes  fancy words that I just used above (abundant and undulating) . When I read the formal or main stream Number Theory , an average book on number theory would deal with primes, rational, irrational, composites , highly composite etc. numbers. I have never or rarely come across terms like lazy caterer number , evil number , happy number in formal literature on number theory. Now, I understand that these attributes are based on certain characteristics that maybe exhibited by such numbers. However, is it worthwhile to know these attributes or are they just trivial and cursory properties being assigned to numbers that might be lacking depth otherwise? I may be missing out something here that maybe worthwhile . Is it really the case or am I amiss?
 A: For me, the main issue that determines whether one of these classes of numbers is likely to be essentially pointless trivia or whether it is likely to be of interest to mathematicians is: is the property digit-based? 
If "yes", it's almost certainly pointless. Happy, evil, undulating, Kaprekar, etc, numbers are all in this category (albeit evil uses binary digits, which is a slight plus). Being abundant, on the other hand, is about significant properties of the number (its factors), not just about the way we write it. This looks more like a real class of numbers that number theorists might be interested in (and indeed it is).
The lazy caterer numbers (or really, the lazy caterer sequence; incidentally although familiar with the sequence I've never heard that name before) is actually in a third class. Being a lazy caterer number isn't really something that tells you more about the number itself, but it's saying that the number is the solution to some other problem. So these numbers might be interesting to mathematicians, but probably not to number theorists; rather, to whoever might be interested in the original problem.
