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 Common Lisp (SBCL 2.0.3) (judge verdict: Accepted)

(defun sum-of-divisor (n)
  (loop :for i :from n :downto 1
        :with basis = 1 and prev-div = 1 and sum = 0 
        :do (progn
              (unless (= prev-div (floor n i))
                (let ((tmp (floor n i)))
                  (loop :for i :from (+ prev-div 1) :to tmp
                        :do (incf basis i))
                  ;(format t "prev-div: ~A,tmp: ~A~%" prev-div tmp)
                  (setq prev-div tmp)))
              (incf sum (* basis i)))
              ;(format t "index:~A, basis:~A, sum:~A~%" i basis sum))
        :finally (return sum)))

(format t "~A~%" (sum-of-divisor (read)))