Merge pull request #1 from srcerer/patch-1

Create sieve_augmented.clj

Author: timothypratley

notebooks/math/primes/factorization/sieve_augmented.clj

@@ -0,0 +1,31 @@
+(ns math.primes.factorization.sieve-augmented
+  (:require [clojure.math :as m]))
+
+;; Adapts the
+;; [Seive of Eratosthenes](https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes)
+;; to prime factorize numbers through `n`.
+
+(defn prime-factors [n]
+  (reduce
+   (fn [factors prime]
+     (if (= 1 (count (nth factors prime)))
+       (reduce
+        (fn [factors multiple]
+          (let [[composite-divisor :as divisors] (nth factors multiple)]
+            (if (< prime composite-divisor)
+              (let [remaining-divisor (/ composite-divisor prime)
+                    remaining-divisors (nth factors remaining-divisor)
+                    prime-divisors (cons prime (rest divisors))]
+                (assoc
+                 factors multiple
+                 (if (< 1 (count remaining-divisors))
+                   (concat remaining-divisors prime-divisors)
+                   (cons remaining-divisor prime-divisors))))
+              factors)))
+        factors
+        (range (* prime prime) (inc n) prime))
+       factors))
+   (mapv list (range (inc n)))
+   (range 2 (inc (m/sqrt n)))))
+
+(prime-factors 10)