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 Go (1.14.1) (judge verdict: Time Limit Exceeded)

package main

import (
	"bufio"
	"fmt"
	"os"
	"strconv"
)

const (
	initialBufSize = 100000
	maxBufSize     = 10000000
)

var (
	sc = bufio.NewScanner(os.Stdin)
	wt = bufio.NewWriter(os.Stdout)
)

func next() string {
	sc.Scan()
	return sc.Text()
}

func nextInt() int {
	i, _ := strconv.Atoi(next())
	return i
}

func nextInt2() (int, int) {
	return nextInt(), nextInt()
}

func nextInt3() (int, int, int) {
	return nextInt(), nextInt(), nextInt()
}

func nextInt4() (int, int, int, int) {
	return nextInt(), nextInt(), nextInt(), nextInt()
}

func nextInts(n int) []int {
	slice := make([]int, n)
	for i := 0; i < n; i++ {
		slice[i] = nextInt()
	}
	return slice
}

func nextFloat64() float64 {
	f, _ := strconv.ParseFloat(next(), 64)
	return f
}

func nextFloat64s(n int) []float64 {
	slice := make([]float64, n)
	for i := 0; i < n; i++ {
		slice[i] = nextFloat64()
	}
	return slice
}

func putf(format string, a ...interface{}) {
	fmt.Fprintf(wt, format, a...)
}

func puts(a ...interface{}) {
	fmt.Fprintln(wt, a...)
}

func minFactors(n int) []int {
	mf := make([]int, n+1)
	for i := range mf {
		mf[i] = i
	}
	for i := 2; i*i <= n; i++ {
		if mf[i] != i {
			continue
		}
		for j := i * i; j <= n; j += i {
			if mf[j] == j {
				mf[j] = i
			}
		}
	}
	return mf
}

func main() {
	sc.Split(bufio.ScanWords)
	sc.Buffer(make([]byte, initialBufSize), maxBufSize)
	defer wt.Flush()

	n := nextInt()

	mf := minFactors(n)

	ans := 0
	for i := 1; i <= n; i++ {
		mp := map[int]int{}
		for j := i; j > 1; j /= mf[j] {
			mp[mf[j]]++
		}
		add := 1
		for _, v := range mp {
			add *= v + 1
		}
		ans += i * add
	}

	puts(ans)
}