Question

Problem 1. Given any set A = {a1, a2, a3, a4} of four distinct positive integers, we denote the sum
a1 +a2 +a3 +a4 by sA. Let nA denote the number of pairs (i, j) with 1  i < j  4 for which ai +aj
divides sA. Find all sets A of four distinct positive integers which achieve the largest possible value
of nA.