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: Time Limit Exceeded)

(declaim (inline divisor?))
(defun divisor? (n m)
  (zerop (mod m n)))

(let ((n (read)))
  (princ (loop :for k :from 1 :to n
               :sum (* k
                       (1+ (loop :for i :from 1 :to (if (evenp k) (/ k 2) (/ (1- k) 2))
                                 :count (divisor? i k)))))))