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use num_prime::nt_funcs::factorize64;
/// Return all divisors of the target
fn divisors(target: u64) -> Vec<u64> {
let factors = factorize64(target);
let mut result = Vec::with_capacity(factors.iter().map(|(_, e)| e + 1).product());
result.push(1);
for (p, e) in factors {
// the new results contain all previous divisors multiplied by p, p^2, .., p^e
let mut new_result = Vec::with_capacity(result.len() * e);
for i in 1..(e as u32 + 1) {
new_result.extend(result.iter().map(|f| f * p.pow(i)));
}
result.append(&mut new_result);
}
result
}
/// Calculate the divisor sigma function σ_z(n) on the target
/// Reference: <https://en.wikipedia.org/wiki/Divisor_function>
fn divisor_sigma(target: u64, z: u32) -> u64 {
divisors(target).into_iter().map(|d| d.pow(z)).sum()
}
fn main() {
println!("Divisor sigma with z=1 of numbers from 10 to 99:");
for i in 10..100 {
println!("{}: {:?}", i, divisor_sigma(i, 1));
}
}
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