If n = xy then n-1 = (x-1) + (y-1) + (x-1)(y-1), x & y need not be coprime. If there are 3 factors of n, say n = xyz then is there a general form s.t. (x-1), (y-1) and (z-1) combine to sum to (n-1) and do x, y & z have to be (pairwise) coprime? (n-1) = (x-1) + (y-1) + (z-1) + (x-1)(y-1) + (x-1)(z-1) + (y-1)(z-1) + (x-1)(y-1)(z-1)?
What about 4 factors, etc.? Where could I find a proof? Thanks!