Data commit

Task/Almost-prime/Clojure/almost-prime.clj

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+(ns clojure.examples.almostprime
+	(:gen-class))
+
+(defn divisors [n]
+    " Finds divisors by looping through integers 2, 3,...i.. up to sqrt (n) [note: rather than compute sqrt(), test with i*i <=n] "
+    (let [div (some #(if (= 0 (mod n %)) % nil) (take-while #(<= (* % %) n) (iterate inc 2)))]
+        (if div                                                         ; div = nil (if no divisor found else its the divisor)
+            (into [] (concat (divisors div) (divisors (/ n div))))      ; Concat the two divisors of the two divisors
+            [n])))                                                      ; Number is prime so only itself as a divisor
+
+(defn divisors-k [k n]
+    " Finds n numbers with k divisors.  Does this by looping through integers 2, 3, ... filtering (passing) ones with k divisors and
+      taking the first n "
+    (->> (iterate inc 2)            ; infinite sequence of numbers starting at 2
+         (map divisors)             ; compute divisor of each element of sequence
+         (filter #(= (count %) k))  ; filter to take only elements with k divisors
+         (take n)                   ; take n elements from filtered sequence
+         (map #(apply * %))))       ; compute number by taking product of divisors
+
+(println (for [k (range 1 6)]
+          (println "k:" k (divisors-k k 10))))
+
+}