Count in factors: Difference between revisions

=={{header|Common Lisp}}==

Auto extending prime list:

<lang lisp>(defparameter *primes*

(make-array 10 :adjustable t :fill-pointer 0 :element-type 'integer))

(mapc #'(lambda (x) (vector-push x *primes*)) '(2 3 5 7))

(defun extend-primes (n)

(let ((p (+ 2 (elt *primes* (1- (length *primes*))))))

(loop for i = p then (+ 2 i)

while (<= (* i i) n) do

(if (primep i t) (vector-push-extend i *primes*)))))

(defun primep (n &optional skip)

(if (not skip) (extend-primes n))

(if (= n 1) nil

(loop for p across *primes* while (<= (* p p) n)

never (zerop (mod n p)))))

(defun factors (n)

(extend-primes n)

(loop with res for x across *primes* while (> n (* x x)) do

(loop while (zerop (rem n x)) do

(setf n (/ n x))

(push x res))

finally (return (if (> n 1) (cons n res) res))))

(loop for n from 1 do

(format t "~a: ~{~a~^ × ~}~%" n (reverse (factors n))))</lang>output<lang>1:

2: 2

3: 3

4: 4

5: 5

6: 2 × 3

7: 7

8: 2 × 2 × 2

9: 9

10: 2 × 5

11: 11

12: 2 × 2 × 3

13: 13

14: 2 × 7

...</lang>