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: Time Limit Exceeded)

object Main extends App {
  val inputs: Seq[String] = scala.io.Source.stdin.getLines().toList
  val n = inputs.head.toInt

  println(solve(n))

  def solve(n: Int): Long = {
    val nums = scala.collection.mutable.ArrayBuffer.fill(n+1)(0)
    var ans = 0L

    (1 to n).foreach { i =>
      (1 to i).foreach { j =>
        if (i % j == 0) nums.update(i, nums(i) + 1)
      }
    }

    (1 to n).foreach { i =>
      ans = ans + nums(i) * i
    }
    return ans
  }
}