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 Rust (1.42.0) (judge verdict: Accepted)

use std::*;
use std::io::{stderr, stdin, stdout, BufReader, BufWriter, Cursor, Read, Write};
use std::iter::Iterator;
use std::str::FromStr;
#[allow(unused_imports)]
use std::fmt::{Display, Formatter};

#[allow(dead_code)]
fn main() {
  let stdin = stdin();
  let r = &mut BufReader::new(stdin.lock());
  let stdout = stdout();
  let w = &mut BufWriter::new(stdout.lock());
  let stderr = stderr();
  let err = &mut BufWriter::new(stderr.lock());
  run(r, w, err);
  w.flush().unwrap();
  err.flush().unwrap();
}

macro_rules! _ft { () => (impl FnOnce(&mut Cursor<Vec<u8>>, &mut Vec<u8>, &mut Vec<u8>)); }

#[allow(dead_code)]
fn test(input: &str, output: &str, f: _ft!()) {
  let r = &mut Cursor::new(input.as_bytes().to_vec());
  let w: &mut Vec<u8> = &mut Vec::new();
  let err: &mut Vec<u8> = &mut Vec::new();
  f(r, w, err);
  let mut stderr = stderr();
  writeln!(stderr, "{}", String::from_utf8(err.to_vec()).unwrap()).unwrap();
  stderr.flush().ok();
  assert_eq!(String::from_utf8(w.to_vec()).unwrap(), output)
}

#[allow(dead_code)]
macro_rules! t {
  ($f: ident => $input: expr, $output: expr) => (
    #[test]
    fn $f() { test($input, $output, run); }
  );
}

macro_rules! _display_st {
    ($f: expr; $name: expr, ) => (write!($f, "{}", $name)?);
    ($f: expr; $name: expr) => (_display_st!($f; $name, ));
    ($f: expr; $name: expr, $($rest: expr),+, ) => (
      _display_st!($f; $name);
      write!($f, " ")?;
      _display_st!($f; $($rest, )+);
    );
    ($f: expr; $name: expr, $($rest: expr),+) => (_display_st!($f; $name, $($rest, )+));
}

/// 構造体を作成する
#[allow(unused_macros)]
macro_rules! st {
  ($name: ident => $($p: ident : $t: ty),+) => (
    struct $name { $($p : $t),+ }
    impl FromStr for $name {
      type Err = ();
      fn from_str(s: &str) -> Result<Self, Self::Err> {
        let mut iter = s.split_whitespace();
        Ok(Self {
          $($p: iter.next().unwrap().parse::<$t>().unwrap(),)+
        })
      }
    }
    impl Display for $name {
      fn fmt(&self, f: &mut Formatter<'_>) -> std::fmt::Result {
        _display_st!(f; $(&self.$p, )+);
        Ok(())
      }
    }
  );
  ($name: ident => $($($p: ident),+: $t: ty);+) => (st!($name => $($($p : $t),+),+););
  ($name: ident => $($($p: ident),+: $($t: ty),+);+) => (st!($name => $($($p : $t),+),+););
  ($name: ident => $($p: ident),+: $t: ty) => (st!($name => $($p : $t),+););
  ($name: ident => $($p: ident),+: $($t: ty),+) => (st!($name => $($p : $t),+););
}

fn _read_iter<R: Read>(reader: &mut R) -> impl Iterator<Item=char> + '_ {
  reader.by_ref()
    .bytes()
    .map(|c| c.unwrap() as char)
    .skip_while(|c| c.is_whitespace())
}

#[allow(dead_code)]
fn read<F: FromStr, R: Read>(reader: &mut R) -> F {
  let str = _read_iter(reader).take_while(|c| !c.is_whitespace()).collect::<String>();
  str.parse::<F>().ok().unwrap()
}

#[allow(dead_code)]
fn read_line<F: FromStr, R: Read>(reader: &mut R) -> F {
  let str = _read_iter(reader).take_while(|c| c != &'\n').collect::<String>();
  let str = if str.ends_with('\r') { &str[0..str.len() - 1] } else { &str };
  str.parse::<F>().ok().unwrap()
}

#[allow(dead_code)]
fn read1<R: Read, T>(reader: &mut R, mut f: impl FnMut(char) -> T) -> T {
  f(_read_iter(reader).next().unwrap())
}

#[allow(dead_code)]
fn read1_line<R: Read, T>(reader: &mut R, f: impl FnMut(char) -> T) -> Vec<T> {
  _read_iter(reader).take_while(|c| c != &'\n').map(f).collect::<Vec<_>>()
}

/// 1要素読む
#[allow(unused_macros)]
macro_rules! r {
  ($stream: expr) => (read::<String, _>($stream));
  ($stream: expr, ) => (r!($stream));
  ($stream: expr; ) => (r!($stream));

  ($stream: expr; $t: ty) => (read::<$t, _>($stream));
  ($stream: expr; $t: ty; 1~) => (r!($stream; $t) - 1);

  ($stream: expr; $($t: ty),+) => (($(r!($stream; $t)),*));
  ($stream: expr; $($t: ty),+; 1~) => (($(r!($stream; $t) - 1),*));

  ($stream: expr; $t: ty; $n: expr) => (
    (0..$n).map(|_| r!($stream; $t)).collect::<Vec<_>>()
  );
  ($stream: expr; $t: ty; $n: expr; 1~) => (
    (0..$n).map(|_| r!($stream; $t) - 1).collect::<Vec<_>>()
  );

  ($stream: expr; $t: ty; $h: expr, $w: expr) => (
    (0..$h).map(|_| (0..$w).map(|_| r!($stream; $t)).collect::<Vec<_>>()).collect::<Vec<_>>()
  );
  ($stream: expr; $t: ty; $h: expr, $w: expr; 1~) => (
    (0..$h).map(|_| (0..$w).map(|_| r!($stream; $t) - 1).collect::<Vec<_>>()).collect::<Vec<_>>()
  );
}

/// 1文字読む
#[allow(unused_macros)]
macro_rules! r1 {
  ($stream: expr) => (read1($stream, |c| c));
  ($stream: expr, ) => (r!($stream));
  ($stream: expr; ) => (r!($stream));
  ($stream: expr; $f: expr) => (read1($stream, $f));
  ($stream: expr; $f: expr; $n: expr) => ((0..$n).map(|_| r1!($stream; $f)).collect::<Vec<_>>());
  ($stream: expr; $f: expr; $h: expr, $w: expr) => (
    (0..$h).map(|_| (0..$w).map(|_| r1!($stream; $f)).collect::<Vec<_>>()).collect::<Vec<_>>()
  );
}

/// 1行読む
#[allow(unused_macros)]
macro_rules! rl {
  ($stream: expr) => (read_line::<String, _>($stream));
  ($stream: expr, ) => (r!($stream));
  ($stream: expr; ) => (r!($stream));
  ($stream: expr; $t: ty) => (read_line::<$t,  _>($stream));
  ($stream: expr; $t: ty; $n: expr) => ((0..$n).map(|_| rl!($stream; $t)).collect::<Vec<_>>());
}

macro_rules! _writes {
  ($stream: expr; $arg0: expr, $($arg: expr),*) => ({
    write!($stream, "{}", $arg0).ok();
    $(write!($stream, " {}", $arg).ok();)*
  });
}

/// 変数を出力
#[allow(unused_macros)]
macro_rules! w {
  ($stream: expr) => (write!($stream, " ").ok());
  ($stream: expr; ) => (w!($stream));
  ($stream: expr, ) => (w!($stream));

  ($stream: expr; $arg: expr) => (write!($stream, "{}", $arg).ok());
  ($stream: expr; $arg: expr, ) => (w!($stream; $arg));

  ($stream: expr; $arg0: expr, $($arg: expr),+) => (_writes!($stream; $arg0, $($arg),+));
  ($stream: expr; $arg0: expr, $($arg: expr),+, ) => (w!($stream; $arg0, $($arg),*));

  ($stream: expr, $($arg: tt)*) => (write!($stream, $($arg)*).ok());
}

/// 変数を改行付きで出力
#[allow(unused_macros)]
macro_rules! wl {
  ($stream: expr) => (writeln!($stream).ok());
  ($stream: expr, ) => (wl!($stream));
  ($stream: expr; ) => (wl!($stream));

  ($stream: expr; $arg: expr) => (writeln!($stream, "{}", $arg).ok());
  ($stream: expr; $arg: expr, ) => (wl!($stream; $arg));

  ($stream: expr; $arg0: expr, $($arg: expr),+) => ({
    _writes!($stream; $arg0, $($arg),+);
    wl!($stream)
  });
  ($stream: expr; $arg0: expr, $($arg: expr),+, ) => (wl!($stream; $arg0, $($arg),*));

  ($stream: expr, $($arg: tt)*) => (writeln!($stream, $($arg)*).ok());
}

/// ベクタを出力
#[allow(unused_macros)]
macro_rules! w_vec {
  ($stream: expr; $vec: expr) => ({
    let mut iter = $vec.iter();
    match iter.next() { Some(&i) => { w!($stream; i); }, None => {}, }
    for &i in iter { w!($stream; i); }
  });

  ($stream: expr; $vec: expr; $n: expr) => (w_vec!($stream; $vec => |e| e, " "; $n));
  ($stream: expr; $vec: expr => $f: expr; $n: expr) => (w_vec!($stream; $vec => $f, ""; $n));
  ($stream: expr; $vec: expr => $f: expr, $del: expr; $n: expr) => (
    w!($stream; $f($vec[0]));
    for i in 1..$n { w!($stream, "{}{}", $del, $f($vec[i as usize])); }
  );
}

/// ベクタを改行付きで出力
#[allow(unused_macros)]
macro_rules! wl_vec {
  ($stream: expr; $vec: expr) => (for &i in $vec.iter() { wl!($stream; i); });

  ($stream: expr; $vec: expr; $n: expr) => (wl_vec!($stream; $vec => |e| e; $n));
  ($stream: expr; $vec: expr => $f: expr; $n: expr) => (
    for i in 0..$n { wl!($stream; $f($vec[i as usize])); }
  );

  ($stream: expr; $vec: expr; $h: expr, $w: expr) => (wl_vec!($stream; $vec => |e| e, " "; $h, $w));
  ($stream: expr; $vec: expr => $f: expr; $h: expr, $w: expr) => (
    wl_vec!($stream; $vec => $f, ""; $h, $w)
  );
  ($stream: expr; $vec: expr => $f: expr, $del: expr; $h: expr, $w: expr) => (
    for i in 0..$h {
      w!($stream; $f($vec[i as usize][0]));
      for j in 1..$w { w!($stream, "{}{}", $del, $f($vec[i as usize][j as usize])); }
      wl!($stream);
    }
  );
}

#[allow(unused_variables)]
fn run<R: Read, W: Write, E: Write>(r_: &mut R, w_: &mut W, err: &mut E) {
  let n = r!(r_; u128);
  let mut ans = 0u128;
  for i in 1..n + 1 {
    let m = n / i;
    ans += i * m * (m + 1) / 2;
  }
  w!(w_; ans);
}

t!(td1 => r"4", r"23");
t!(td2 => r"100", r"26879");
t!(td3 => r"10000000", r"838627288460105");
t!(td4 => r"", r"");