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 Julia (1.4.0) (judge verdict: Accepted)

rl() = [parse(Int64, x) for x in split(readline())]

function solve()
    N, = rl()

    r = zeros(Int64, N)
    r[1] = 1
    for p in 2:N
        n = pn = 1
        while pn <= N
            pn *= p
            n += 1
        end
        while true
            pn = div(pn, p)
            n -= 1
            if pn <= 1
                break
            end
            a = 1
            apn = pn
            while apn <= N
                if r[a] > 0 && r[apn] == 0
                    r[apn] = r[a] * n * pn
                end
                a += 1
                apn += pn
            end
        end
    end

    sum(r)
end

println(solve())