(defn maxmul7
    "A function to return the greatest multiple of 7 in a defined range inclusive"
    [min max]
    (if (and (and (>= max 7) (<= min (- max (mod max 7)))) (>= min 7)) (- max (mod max 7)) nil)
)

(maxmul7 15 21)



(defn sumcube [min max]
    "A function to sum the cubes in a given range inclusive"
    (loop [step min total 0]
        (if (< max step)
            total
            (recur (inc step) (+ total (Math/pow step 3)))
        )
    )
)


(sumcube 1 3)

(defn drop2nd
    [plist]
    (if (< (count plist) 3)
        (println "less than three")
        ;greater than or equal to three
        (loop [step 0 nlist '()]
            (if (< step (- (count plist) 0))
                (if (= step 1)
                    (recur (inc step) nlist)
                    (recur (inc step) (conj nlist (nth plist step)))
                )
                nlist
            )
        )
    )
)

(drop2nd '(1 2 3 4 5))

(defn devisors
    [num]
    (loop [step 1 plist '()]
        (if (<= step (/ num 2) )
            (if (= 0 (mod num step))
                (recur (inc step) (conj plist step))
                (recur (inc step) plist)
            )
            plist
        )
    )
)
(defn sumList
    [plist]
    (loop [step 0 total 0]
        (if (<= step (count plist))
            (recur (inc step) (+ total step))
            total
        )
    )
)
(defn perfect
    [num]
    (if (= num (sumList (devisors num)))
        true
        false
    )

)

(perfect 6)


(defn ave
  [plist]
  (/ (sumList plist) (count plist))
)

(defn sumXMSquared
  [plist]
  (let [mean (ave plist)]
    (loop [step 0 total 0]
      (if (< step (count plist))
        (recur (inc step) (+ total (Math/pow (- (nth plist step) mean) 2) ) )
        total
      )
    )
  )
)

(defn stdDiv
  [plist]
  (Math/sqrt (/ (sumXMSquared plist) (- (count plist) 1)) )
)

(ave '(1 2 3 4 5))

(stdDiv '(1 2 3 4))


(defn occur
  [el coll]
  (loop [step 0]
    (if (< step (count coll))
      (if (= el (nth coll step))
        step
        (recur (inc step))
      )
      nil
    )
  )
)

(occur 7 '(1 2 3 4 5))