racket prime factorization

prime-factors.rkt

(define (eratosthenes n)
  (define (sift list p)
    (filter (lambda (n)
              (not (zero? (modulo n p))))
            list))
  (define (iter nums primes)
    (let ((p (car nums)))
      (if (> (* p p) n)
          (append (reverse primes) nums)
          (iter (sift (cdr nums) p) (cons p primes)))))
  (iter (cdr (build-list n add1)) '()))

(define (divides? p q)
  (zero? (modulo q p)))

(define (prime-factors n)
  (let loop ((primes (eratosthenes n)))
    (cond ((memq n primes) (list n))
          ((divides? (car primes) n)
           (cons (car primes) (prime-factors (/ n (car primes)))))
          (else (loop (cdr primes))))))