The problem was : For a given positive integer N, what is the maximum sum of distinct numbers such that the Least Common Multiple of all these numbers is N. for n=1) Only possible number is 1, so the maximum sum of distinct numbers is exactly 1.
for n= 2 The distinct numbers you can have are just 1 and 2, so the sum is 3. If we consider any other number greater than 2, then the least common multiple will be more than 2.