Kata

Consider the following:

• The divisors of 6 are: 1, 2, 3 & 6 and their sum is 12. Now, 12/6 = 2.
• The divisors of 28 are 1, 2, 4, 7, 14 & 28 and their sum is 56. Now, 56/28 = 2.
• The divisors of 496 are 1, 2, 4, 8, 16, 31, 62, 124, 248, 496 and their sum is 992. Now, 992/496 = 2.

We shall say that (6,28,496) is a grouping with a ratio of 2.

Similarly, consider the grouping (30,140):

• The divisors of 30 are: 1, 2, 3, 5, 6, 10, 15 & 30 and their sum is 72. Now, 72/30 = 12/5 = 2.4.
• The divisors of 140 are 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, 140 and their sum is 336. Now, 336/140 = 12/5 = 2.4.

We shall say that (30,140) is a grouping with a ratio of 12/5.

(6,28) and (30,140) are the only groupings in which every member of a group is 0 <= n < 200. The sum of the smallest members of each group is 6 + 30 = 36.

Given a range(a,b), return the sum of the smallest members of each group. As illustrated above:

• every member of a group must be greater than or equal to a and less than b.
• a group must have 2 or more members.

Examples:
solve(1,200) = 36, the sum of [6,30] as explained above
solve(1,250) = 168, the sum of [6, 12, 30, 40, 80]
solve(1,500) = 498, the sum of [6, 12, 30, 40, 66, 78, 80, 84, 102]

As you can see, for "solve(1,500)", we do not include all (6,28) & (6,496) & (28,496). We count the group once by including 6 only.

If there are no groups, return 0. Upper limit is 2000.

Good luck!

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Simple division

Sub-array division