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A number is perfect if it is equal to the sum of its divisors, the ones that are smaller than it. For example, number 28 is perfect because 28 = 1 + 2 + 4 + 7 + 14.
Motivated by this definition, we introduce the metric of imperfection of number N, denoted with f(N), as the absolute difference between N and the sum of its divisors less than N. It follows that perfect numbers’ imperfection score is 0, and the rest of natural numbers have a higher imperfection score. For example:
Write a programme that, for positive integers A and B, calculates the sum of imperfections of all numbers between A and B: f(A) + f(A + 1) + ... + f(B).
The first line of input contains the positive integers A and B (1 ≤ A ≤ B ≤ 107 ).
The first and only line of output must contain the required sum.
1 + 1 + 2 + 1 + 4 + 0 + 6 + 1 + 5.