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(define (square x) (* x x))
(define (power x n)
(if (= n 0)
1
(* x (power x (- n 1)))))
(define (first-divisor x)
(define (try-iter d)
(cond ((= 0 (remainder x d)) d)
((> (square d) x) x)
(else (try-iter (+ d 1)))))
(try-iter 2))
(define (divexp x d)
(if (= (remainder x d) 0)
(+ (divexp (/ x d) d) 1)
0))
(define (ndiv n)
(define (pair d)
(cons (divexp n d) (/ n (expt d (divexp n d)))))
(if (= n 1) 1
(let ((fd (first-divisor n)))
(* (+ 1 (car (pair fd)))
(ndiv (cdr (pair fd)))))))
(define (kth-factor-triangle-over-n n)
(define (n-fac-tri n)
(if (even? n)
(* (ndiv (/ n 2)) (ndiv (+ n 1)))
(* (ndiv n) (ndiv (/ (+ n 1) 2)))))
(define (try-iter i)
(if (> (n-fac-tri i) n)
i
(try-iter (+ i 1))))
(try-iter 1))
(display
((lambda (x) (/ (* x (+ x 1)) 2))
(kth-factor-triangle-over-n 500)))
(newline)
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