Let f(n) be the maximum positive integer m such that the sum of all positive divisors of m is less than or equal to n. Find all positive integers k such that there are infinitely many positive integers n satisfying the equation n-f(n)=k.

The best solution was submitted by Taeho Kim (김태호), 2011학번. Congratulations!

Here is his Solution of Problem 2011-17.

Alternative solutions were submitted by 김범수 (수리과학과 2010학번, +3), 서기원 (수리과학과 2009학번, +3), 박승균 (수리과학과 2008학번, +3), 장경석 (2011학번, +3), 구도완 (해운대고등학교 3학년, +3), 손동현 (유성고등학교 2학년, +2), 어수강 (서울대학교 석사과정, +2).

Update: I forgot to add 최민수 (2011학번, +3) into the list of people submitted alternative solutions.