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