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'

class Prime
    def each_divisor(n, &block)
        pf = prime_division(n)
        num = -> { pf.inject(1) { |prod, (_, exp)| prod * exp.succ } }
        Enumerator.new(num) { |y| __each_divisor__(1, pf, &y.method(:<<)) }
                  .tap { |enum| enum.each(&block) }
    end

    private def __each_divisor__(d, ary, &block)
        return yield(d) if ary.empty?

        ary = ary.dup
        prime, exp = ary.pop
        0.upto(exp) { __each_divisor__(d, ary, &block); d *= prime }
    end
end

N = gets.to_i

prime = Prime.instance
res = 0
(1..N).each do |i|
  res += i * prime.each_divisor(i).size
end
p res