#[allow(unused_imports)] use std::cmp::*; #[allow(unused_imports)] use std::collections::*; use std::io::{Write, BufWriter}; // https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8 macro_rules! input { ($($r:tt)*) => { let stdin = std::io::stdin(); let mut bytes = std::io::Read::bytes(std::io::BufReader::new(stdin.lock())); let mut next = move || -> String{ bytes .by_ref() .map(|r|r.unwrap() as char) .skip_while(|c|c.is_whitespace()) .take_while(|c|!c.is_whitespace()) .collect() }; input_inner!{next, $($r)*} }; } macro_rules! input_inner { ($next:expr) => {}; ($next:expr, ) => {}; ($next:expr, $var:ident : $t:tt $($r:tt)*) => { let $var = read_value!($next, $t); input_inner!{$next $($r)*} }; } macro_rules! read_value { ($next:expr, ( $($t:tt),* )) => { ( $(read_value!($next, $t)),* ) }; ($next:expr, [ $t:tt ; $len:expr ]) => { (0..$len).map(|_| read_value!($next, $t)).collect::>() }; ($next:expr, chars) => { read_value!($next, String).chars().collect::>() }; ($next:expr, usize1) => { read_value!($next, usize) - 1 }; ($next:expr, [ $t:tt ]) => {{ let len = read_value!($next, usize); (0..len).map(|_| read_value!($next, $t)).collect::>() }}; ($next:expr, $t:ty) => { $next().parse::<$t>().expect("Parse error") }; } #[allow(unused)] macro_rules! debug { ($($format:tt)*) => (write!(std::io::stderr(), $($format)*).unwrap()); } #[allow(unused)] macro_rules! debugln { ($($format:tt)*) => (writeln!(std::io::stderr(), $($format)*).unwrap()); } fn solve() { let out = std::io::stdout(); let mut out = BufWriter::new(out.lock()); macro_rules! puts { ($($format:tt)*) => (let _ = write!(out,$($format)*);); } input! { n: usize, a: [usize], } let n = n + 1; // Problem: find \sum_{x: a} \sum_{j = 1}^x (gcd(x, j) - 1) let mut phi = vec![1i64; n]; let mut fac = vec![0; n]; for i in 1..n { fac[i] = i; } for i in 2..n { if fac[i] != i { continue; } for j in 2..(n - 1) / i + 1 { fac[i * j] = i; } } for i in 1..n { let mut v = i; let mut a = 1; while v > 1 { let p = fac[v]; let mut e = 0; while v % p == 0 { e += 1; v /= p; } a *= p - 1; for _ in 0..e - 1 { a *= p; } } phi[i] = a as i64; } // \sum_[j = 1}^x gcd(x, i) = \sum_{g | x} g * phi(x / g) let mut vals = vec![0; n]; for g in 1..n { for j in 1..(n - 1) / g + 1 { vals[g * j] += g as i64 * phi[j]; } } let mut tot = 0; // (RHS) = \sum {x: a} vals[x] - x for a in a { tot += vals[a] - a as i64; } puts!("{}\n", tot); } fn main() { // In order to avoid potential stack overflow, spawn a new thread. let stack_size = 104_857_600; // 100 MB let thd = std::thread::Builder::new().stack_size(stack_size); thd.spawn(|| solve()).unwrap().join().unwrap(); }