Sum of The Positive Integral Divisors
Posted: Tue Feb 12, 2013 7:08 pmOkay, I know how to solve this, but does anybody know why the trick works? I am probably overlooking something simple, but an explanation would be very much appreciated. :D
The shortcut is to multiply the terms [unparseable or potentially dangerous latex formula] for each term [unparseable or potentially dangerous latex formula] in the prime factorization of a number [unparseable or potentially dangerous latex formula].
Expanding this out, you get [unparseable or potentially dangerous latex formula] [unparseable or potentially dangerous latex formula][unparseable or potentially dangerous latex formula]
This is somewhat difficult to see at first, but if you expanded this out fully, you would get the sum of all possible products of combinations of powers (likely badly worded there) that divide [unparseable or potentially dangerous latex formula], which ultimately gives you the sum of all of the positive integral divisors of [unparseable or potentially dangerous latex formula].