Too many remainders

One day, Chris wanted to challenge Pi's magical powers.

Chris: I have divided 2016 by a positive integer. Do you know what the remainder is?

Pi: I can try, but I only have a 1 in 1009 chance of getting it correct.

Chris: Then, there must be 1009 of them. Do you know what their sum is?

Pi: Of course, I do!

Pi knew the sum of all possible values of remainders when 2016 was divided by some natural number. Do you?

Submit your answer as this sum.


Inspired by Pi Han Goh.
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