;; Change language to "Advanced Student" to run!

;; divs_of_120:  --> natNum
;;Count all the positive divisors 120
(define (divs_of_120)
  (divs_of_120_help 120))

;; divs_of_120_help: natNum --> natNum
;; Count all the positive divisors of 120 
;; that are less than or equal to n.
(define (divs_of_120_help n)
  (cond 
    [(zero? n) 0]
    [else (+ (cond
               [(= 0 (modulo 120 n)) 1]
               [else 0]) (divs_of_120_help (sub1 n)))]))

"divs_of_120 test cases:"
(= 16 (divs_of_120))

;; divs_of:  natNum --> natNum
;;Count all the positive divisors n0 
(define (divs_of n0)
  (divs_of_help n0 n0))

;; divs_of_help: natNum, natNum --> natNum
;; Count all the positive divisors of n0 
;; that are less than or equal to n.
(define (divs_of_help n0 n)
  (cond 
    [(zero? n) 0]
    [else (+ (cond
               [(= 0 (modulo n0 n)) 1]
               [else 0]) (divs_of_help n0 (sub1 n)))]))


"divs_of test cases:"
(= 0 (divs_of 0))
(= 1 (divs_of 1))
(= 2 (divs_of 3))
(= 6 (divs_of 12))
(= 2 (divs_of 37))
(= 16 (divs_of 120))