Problem:
Score : 400 points

Problem Statement

For a positive integer X, let f(X) be the number of positive divisors of X.

Given a positive integer N, find \sum_{K=1}^N K\times f(K).

Constraints

1 \leq N \leq 10^7

Input

Input is given from Standard Input in the following format:

N

Output

Print the value \sum_{K=1}^N K\times f(K).

Sample Input 1

4

Sample Output 1

23

We have f(1)=1, f(2)=2, f(3)=2, and f(4)=3, so the answer is 1\times 1 + 2\times 2 + 3\times 2 + 4\times 3 =23.

Sample Input 2

100

Sample Output 2

26879

Sample Input 3

10000000

Sample Output 3

838627288460105

Watch out for overflows.

Solution in Scala (2.13.1) (judge verdict: Accepted)

object Main extends App {
    val stdin = new java.util.Scanner(new java.io.BufferedInputStream(System.in))
    val stdout = new java.io.PrintWriter(new java.io.BufferedOutputStream(System.out))

    while (stdin.hasNext()) {
        val foo = stdin.nextInt()
        var bar : Long = 0
        for (i <- 1 to foo) {
            val x : Long = i
            val k : Long = foo / x
            bar += (x + x * k) * k / 2
        }
        stdout.printf("%d\n", bar.asInstanceOf[java.lang.Long])
    }

    stdin.close()
    stdout.close()
}