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 Haskell (GHC 8.8.3) (judge verdict: Time Limit Exceeded)

import Data.List (group)


primes =
    let
        f (p : ps) = p : (filter $ (/= 0) . (`mod` p)) ps
    in
        f [ 2 .. ]

primeFactors n = [ x | x <- takeWhile (\y -> y * y <= n) primes, n `mod` x == 0 ]

factorize 1 = []
factorize n =
    let
        x = case primeFactors n of
            []     -> n
            p : ps -> p
    in
        x : factorize (n `div` x)

f k = k * (product . map (+ 1) . map length . group . factorize $ k)

toInt :: String -> Int
toInt = read

main = do
    n <- toInt <$> getLine

    print . sum . map f $ [ 1 .. n ]