; your code goes here
 
(define (factors n) ; 2,3,5-wheel
  (let ((wheel (vector 1 2 2 4 2 4 2 4 6 2 6)))
    (let loop ((n n) (f 2) (w 0) (fs (list)))
      (if (< n (* f f)) (reverse (cons n fs))
        (if (zero? (modulo n f))
            (loop (/ n f) f w (cons f fs))
            (loop n (+ f (vector-ref wheel w))
                  (if (= w 10) 3 (+ w 1)) fs))))))
(define (numdiv n)
  (let ((fs (factors n)))
    (let loop ((prev (car fs)) (fs (cdr fs)) (f 2) (d 1))
      (cond ((null? fs) (* d f))
            ((= (car fs) prev) (loop prev (cdr fs) (+ f 1) d))
            (else (loop (car fs) (cdr fs) 2 (* d f)))))))
 
(define (euler12 limit)
  (let loop ((n 1) (tri 1))
    (if (< limit (numdiv tri))
        (list n tri (numdiv tri))
        (loop (+ n 1) (+ tri n 1)))))
 
(display (euler12 500)) (newline)

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