pub fn factorize_factorial(n: usize) -> Vec<usize> {
let mut e = vec![0; n + 1];
let mut v: Vec<_> = (0..=n).collect();
for i in 2..=n {
if v[i] == 1 {
continue;
}
for j in (i..=n).step_by(i) {
while v[j] % i == 0 {
e[i] += 1;
v[j] /= i;
}
}
}
e
}
#[cfg(test)]
mod tests {
use super::*;
#[test]
fn test() {
assert_eq!(factorize_factorial(10), [0, 0, 8, 4, 0, 2, 0, 1, 0, 0, 0,]);
}
}