## December 30, 2008

at
Tuesday, December 30, 2008
Labels:
Computer Science,
Lisp,
Project Euler
Posted by
Billy

Let d(n) be defined as the sum of proper divisors of n (numbers less than n which divide evenly into n).

If d(a) = b and d(b) = a, where a ≠ b, then a and b are an amicable pair and each of a and b are called amicable numbers.

For example, the proper divisors of 220 are 1, 2, 4, 5, 10, 11, 20, 22, 44, 55 and 110 therefore d(220) = 284. The proper divisors of 284 are 1, 2, 4, 71 and 142 so d(284) = 220.

Evaluate the sum of all the amicable numbers under 10000.

(defun divisor-p (num divisor)

"Tests if divisor is a divisor of num"

(zerop (mod num divisor)))

(defun divisors (num)

"Returns a list of num's divisors"

(do ((i 2 (1+ i))

(result '(1)))

((> i (isqrt num)) (remove-duplicates result))

(when (divisor-p num i)

(setf result (append result (list i (/ num i)))))))

(defun sum-divisors (num)

"Sums the divisors of num"

(reduce #'+ (divisors num)))

(defun amicable-p (num)

"Tests if num is amicable"

(let ((divisors-sum (sum-divisors num)))

(when (and (= num (sum-divisors divisors-sum))

(not (= num divisors-sum)))

num)))

(defun amicable-sum (limit)

"Returns the sum of all amicable numbers below limit"

(do ((i 1 (1+ i))

(result 0))

((>= i limit) result)

(when (amicable-p i)

(incf result i))))

(defun euler-21 ()

(amicable-sum 10000))

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