// ---------- begin input macro ---------- // reference: https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8 macro_rules! input { (source = $s:expr, $($r:tt)*) => { let mut iter = $s.split_whitespace(); input_inner!{iter, $($r)*} }; ($($r:tt)*) => { let s = { use std::io::Read; let mut s = String::new(); std::io::stdin().read_to_string(&mut s).unwrap(); s }; let mut iter = s.split_whitespace(); input_inner!{iter, $($r)*} }; } macro_rules! input_inner { ($iter:expr) => {}; ($iter:expr, ) => {}; ($iter:expr, $var:ident : $t:tt $($r:tt)*) => { let $var = read_value!($iter, $t); input_inner!{$iter $($r)*} }; } macro_rules! read_value { ($iter:expr, ( $($t:tt),* )) => { ( $(read_value!($iter, $t)),* ) }; ($iter:expr, [ $t:tt ; $len:expr ]) => { (0..$len).map(|_| read_value!($iter, $t)).collect::>() }; ($iter:expr, chars) => { read_value!($iter, String).chars().collect::>() }; ($iter:expr, bytes) => { read_value!($iter, String).bytes().collect::>() }; ($iter:expr, usize1) => { read_value!($iter, usize) - 1 }; ($iter:expr, $t:ty) => { $iter.next().unwrap().parse::<$t>().expect("Parse error") }; } // ---------- end input macro ---------- fn sqrt_calc(n: u64, mut f: F) where F: FnMut(u64, u64), { let mut r = n; let mut q = 1; loop { let l = n / (q + 1); if l * l <= n { break; } f(r, r - l); r = l; q += 1; } for i in 1..=r { f(i, 1); } } fn run() { input! { n: u64, } const MOD: u64 = 1_000_000_007; let mut ans = 0; sqrt_calc(n, |b, m| { let rem = n / b - 1; ans += m * rem * (n - 2) % MOD; ans += MOD - m * rem % MOD * (rem - 1) % MOD; }); let mut map = std::collections::HashMap::new(); for i in 1.. { if i * i > n { break; } for &q in [i, n / i].iter() { let mut val = 0; sqrt_calc(q, |b, m| { if b > 1 { let rem = q / b - 1; val += m * rem % MOD; } }); map.insert(q, val % MOD); } } sqrt_calc(n, |a, m| { let q = n / a; if q - 1 < 2 { return; } ans += MOD - m * *map.get(&q).unwrap() % MOD; }); ans %= MOD; println!("{}", ans); } fn main() { run(); }