## March 24, 2009

at
Tuesday, March 24, 2009
Labels:
Computer Science,
Lisp,
Project Euler
Posted by
Billy

The sequence of triangle numbers is generated by adding the natural numbers. So the 7th triangle number would be

1 + 2 + 3 + 4 + 5 + 6 + 7 = 28.

The first ten terms would be:

1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ...

Let us list the factors of the first seven triangle numbers:

1: 1

3: 1,3

6: 1,2,3,6

10: 1,2,5,10

15: 1,3,5,15

21: 1,3,7,21

28: 1,2,4,7,14,28

We can see that 28 is the first triangle number to have over five divisors.

What is the value of the first triangle number to have over five hundred divisors?

(defun num-of-divisors (num)

"Returns the number of divisors of num for num > 1"

(let ((square-root (sqrt num))

(result 0))

(do ((x 1 (1+ x)))

((> x square-root) result)

(when (zerop (mod num x))

(setf result (+ 2 result))))))

(defun euler-12 (&optional (tri-num 1) (tri-val 1))

(if (> (num-of-divisors tri-val) 500)

tri-val

(euler-12 (1+ tri-num) (+ 1 tri-num tri-val))))

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