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 Pascal (FPC 3.0.4) (judge verdict: Accepted)

var
	N,i,j,ans:int64;
begin
	read(N);
	i:=1;
	while i<=N do begin
		j:=N div(N div i)+1;
		inc(ans,(j-i)*(i+j-1)*(N div i)*(N div i+1)div 4);
		i:=j;
	end;
	writeln(ans);
end.