3469. Savrsen

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 $B$: $f(A)+f(A+1)+\dots +f(B)$.