Codingame Solution: Sum of divisors

Original Problem

You have to print the sum of divisors of all the numbers from \(1\) to \(n\). It's superfast when you know the trick but you have to find it. For example if \(n=4\), lets define \(d(n)\) the set of the divisors of n:

• d(1)={1}
• d(2)={1,2}
• d(3)={1,3}
• d(4)={1,2,4}

And their sum is \(1+1+2+1+3+1+2+4=15\). Look carefully at the divisors to find the trick.

I solved this problem already and derived the solution here. Implementing the function in JavaScript is pretty straightforward then:

const n = +readline();
let s = n * n;
for (let i = 1; i <= n; i++) {
    s-= n % i;
}
print(s);