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 Ruby (2.7.1) (judge verdict: Time Limit Exceeded)

require 'prime'

n = gets.to_i
f = Array.new(n+1, 1)

2.upto(n) do |i|
    i.step(n, i) do |j|
        f[j] += 1
    end
end

puts f.each_with_index.inject(0) {|r, (v, i)| r += v * i}