; just split up in cases:
; Braun tree with one node has height 0
; Braun tree with two nodes has height 1
; Braun tree with more than two nodes has height exactly one more
;   than the height of its bigger subtree; the numbers below correspond
;   exactly to the size of the bigger subtree (actually, when there's odd
;   number of nodes in the tree, then both subtrees are of equal size, so
;   we can pick any)
(define (braunheight n)
  (cond ((= n 1) 0)
	((= n 2) 1)
	((odd? n) (+ 1 (braunheight (/ (- n 1) 2))))
	((even? n) (+ 1 (braunheight (/ n 2))))
))

; we don't need to test numbers for primality here; if the number is
; divisible by any square, then its not square free
(define (sqfree n)
  (define (aux i n)
    (if (<= i (sqrt n))
	(if (= (modulo n (* i i)) 0)
	    #f
	    (aux (+ i 1) n))
	#t))
  (aux 2 n)
)