3 \(s / 128\) \(MB / 120\) points

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:

●
f(6) = |\(6 - 1 - 2 - 3\)| = 0,
●
f(11) = |\(11 - 1\)| = 10,
●
f(24) = |\(24 - 1 - 2 - 3 - 4 - 6 - 8 - 12\)| = |-12| = 12.

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 ≤ \(A\)

≤ \(B\)

≤ 10 ^{7}{ }).

The first and only line of output must contain the required sum.

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출처 COCI 2016/2017 Contest 6