Clojure Prime Factors

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(defn factors [n] (map #(/ n %) (filter #(zero? (rem n %)) (range 1 (+ n 1)))))

(defn prime? [n] 
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(defn prime-factors [n]
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Depends on what you find simple, right? :) Removing the Math/sqrt optimization might be simpler, but isn’t as efficient. In any case, here’s my take, which is basically the same, but has a few differences that I see as simplifications:

1. Uses the loop construct rather than arity overloading, so clients of the function only have one set of arguments to choose.

2. Uses / instead of quot if the candidate is a divisor.

3. Extracts divisible-by? predicate.

4. Squares the arguments instead of calling directly into Java with Math/sqrt. There’s no risk of overflow because of the way Clojure handles numbers, and this will work with the .NET implementation.

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At the risk of writing C# in Clojure:

(defn factors [n] 
    {:pre [(pos? n) (integer? n)]}
    (loop [n n, s 2, a '()]
        (if-let [f (->> ; find smallest factor
                (range s n) 
                (take-while #(<= % (Math/sqrt n)))
                (filter #(zero? (rem n %)))
                first)]              
            (recur (/ n f) f (conj a f)) ; factor found
            (conj a n))))    ; n is prime

It reduces the branching and is a bit more declarative.

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