Are there numbers that have loop of 3 or more when adding their factors? I know perfect numbers when you add all their factors you get themself (I like to think of this everything important to them adds up to themself)
I know Amicable Number pairs are numbers where you add their factor then do it again will add up to themself. 220 and 284 are examples (I like to think of these pairs as lovers where all that matter to them all add up to the other)
I wonder if there are any numbers where it takes 3 times of adding the factors to get back to themself (like where a number loves another number but that number loves a different number that loves the original number)like a real love triangle
and are their even bigger loops?
can you give me an example of a 3 loop if one exists?
I have no clue how to start to solve this. or prove there is an infinite amount of them.
thanks.