The idea:

Take a whole number .... 44

Write down its factors .... 1, 2, 4, 11, 22, 44

Add the digits of these factors .... 1 + 2 + 4 + 1 + 1 + 2 + 2 + 4 + 4 = 21

Repeat the process with this new number ... 1 , 3, 7, 21 ... 1 + 3 + 7 + 2 + 1 = 14

And again ... 1, 2, 7, 14 ..... 1 + 2 + 7 + 1 + 4 = 15

And again ... 1, 3, 5, 15 ... 1 + 3 + 5 + 1 + 5 = 15

This gives the following diagram:

The question:

Do all positive whole numbers (other than 1 ) end up at 15?

A larger Diagram: