Sum of Imperfections

A number is perfect when it equals the sum of its divisors that are smaller than itself. For example, $28 = 1 + 2 + 4 + 7 + 14$, so 28 is perfect.

Starting from that definition, the imperfection of a natural number $N$, written $f(N)$, is the absolute difference between $N$ and the sum of the divisors of $N$ that are smaller than $N$. A perfect number has imperfection 0, and every other natural number has a positive imperfection. For example:

• $f(6) = |6 - 1 - 2 - 3| = 0$
• $f(11) = |11 - 1| = 10$
• $f(24) = |24 - 1 - 2 - 3 - 4 - 6 - 8 - 12| = |-12| = 12$

Given positive integers $A$ and $B$, write a program that computes the sum of the imperfections of all numbers from $A$ to $B$, that is $f(A) + f(A + 1) + \cdots + f(B)$.

The first line contains the positive integers $A$ and $B$, separated by a space. ($1 \le A \le B \le 10^7$)

Print the required sum on the first and only line.

The sum can exceed the range of a 32 bit integer.