Exercise 3.6

• loop-lab-test.scm contains the definitions related to perfect numbers from pages 58-61 of the text.

• Load these definitions and time the search for perfect number 8128 by running:

       (time (first-perfect-after 496))
  

  This test is included in loop-lab-test.scm.

• Depending on your machine, you will probably see a time of 1000–2000 milliseconds.

• Now do Exercise 3.6. To emphasize that your rewrite is a more efficient version of sum-of-divisors, call your procedure sum-of-divisors-eff.

• Time the search for perfect number 8128 by running:

       (time (first-perfect-after-eff 496))
  

  This test is also included in loop-lab-test.scm. Note that it calls first-perfect-after-eff. It is defined in loop-lab.scm to call perfect-eff?, which calls your sum-of-divisors-eff.

• If you wrote sum-of-divisors-eff correctly, you will see a significant improvement in search time. The time taken should be only 2–5% of the time it took to find 8128 without your changes.