Divisibility problem

[karmic island]

A teacher wrote in one sheet all the remainders of the division of 365 by each of the numbers 1,2,3,⋅⋅⋅, and 365. Then, a student wrote in another sheet all the remainders of the division of 366 by each of the numbers 1,2,3,⋅⋅⋅, and 366. Who owns the sheet whose sum of all the remainders is the greatest, and by how much?

[faint dawn]

For each integer n, the remainder of 365 by n is less than 366 by n by 1 unless n|366

maybe make 2 cases, n that n|366 and n that doesn't.

[karmic island]

ok