There is no reason to it , nothing but it still exists. Mathematics has wonders to do with it
For any natural number take down its divisors including 1 and the number itself. Add the digits of all the divisors. You will get a new number. Do the same over it.
No matter what number u take u fill finally converge to 15 and after that you wont be able to move any further, the number of iterations may vary, and this black hole number 15 when you do the same with it. Lets see what happens.
Divisors of 15 = 1, 3, 5, 15
Add digits = 1+3+5+1+5
Lets take another example you want to take 4 , go for it.
divisors = 1 , 2, 4 Addition = 7 = new number
divisors = 1 , 7 Addition = 8 = new number
divisors = 1 , 2, 4 ,8 Addition = 15 = new number
Back on 15