Why we have to traverse only for last few say 100 maximum elements and check all possible combinations of them only why not we are going till full n^2 in this question any theoretical intuitive or mathematical proof if anyone can explain?

That doesn’t seem correct. There’s a simple counter test. I’m guessing last 200 distinct elements, right?

The total number of maximum divisors can be atmost 128 for any number as `2*3*5*7*11*13*17>10^5`

. So I guess you can get an intuition from it!

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