Given a positive integer n, find the list of positive integers whose product is the largest among all the list whose sum is n. For example, if n is 4 the desired list is 2,2 because 2x2 = 4 is larger than 1x1x1x1 = 1, 2x1x1 = 2 and 3x1 = 3, if n is 5, the desired list is 2, 3.
what is the desired list if n = 2001;
Actually is an algorithm to generate this list. After tried lots of example, i discern(hope am right) for n > 5 its a list of 3's, and a remainder n % 3;
so for n = 2001, I got a list of 667 3's.
If Correct, What property of 3 makes it the ideal integer in that it composes (mostly) this list?.