; helper to return (min min+1 min+2 ... max) as a list
(define (range min max)
  (if (> min max) null
      (cons min (range (+ 1 min) max))))

; returns true if n is divisible by k
(define (divides? n k) (= 0 (modulo n k)))


; a list of pairs of the form (n . #factors)
; used to cache the results of previous calls (memoize)
(define cache '())

(define (count-factors n) 
  ; if I have computed this before, return the old result
  (let ((memory (assoc n cache)))      ; memory = (24 . 8)
    (if memory 
        (cdr memory)
        
        ; else, compute result, remember result, return result
        (let ((result (length 
                       (filter (lambda (k)
                                 (divides? n k)) (range 1 n)))))
          (set! cache (cons (cons n result) cache))
          result))))