[feature] single thread code to calculate hcns using prime factorization

src/main.rs

@@ -1,12 +1,56 @@
 mod sieve;
 
+use std::time::Instant;
+
 use sieve::get_primes;
 
 const MAX_SIEVED_PRIMES: usize = 100_000_000;
 
-fn main() {
+fn count_prime_factor_exponent(prime: u64, mut nr: u64) -> u64 {
-    let primes = get_primes(MAX_SIEVED_PRIMES);
+    let mut count = 0;
+
+    while nr % prime == 0 {
+        nr /= prime;
+        count += 1;
+    }
+
+    count
+}
+
+fn prime_factors(nr: u64, primes: &[u64]) -> u64 {
+    let mut num_teilers = 1;
+
+    let nr_sqrt = (nr as f64).sqrt().ceil() as u64;
+
     for prime in primes {
-        println!("{prime}");
+        if *prime > nr_sqrt {
+            break;
+        }
+
+        let count = count_prime_factor_exponent(*prime, nr);
+        if count > 0 {
+            num_teilers *= count + 1;
+        }
+    }
+
+    num_teilers
+}
+
+fn main() {
+    let start = Instant::now();
+    println!("Precalculating primes...");
+    let primes = get_primes(MAX_SIEVED_PRIMES);
+    println!("{} primes. Took {:?}", primes.len(), start.elapsed());
+
+    let mut max_teilers = 0;
+
+    let start = Instant::now();
+
+    for nr in (2..1_000_000_000).step_by(2) {
+        let teilers = prime_factors(nr, &primes);
+        if teilers > max_teilers {
+            println!("{nr}: {teilers} ({:?} since start)", start.elapsed());
+            max_teilers = teilers;
+        }
     }
 }