The first two consecutive numbers to have two distinct prime factors are:
\[14 = 2 \times 7\] \[15 = 3 \times 5\]
The first three consecutive numbers to have three distinct prime factors are:
\[644 = 2^2 \times 7 \times 23\] \[645 = 3 \times 5 \times 43\] \[646 = 2 \times 17 \times 19\]
Find the first four consecutive integers to have four distinct prime factors each. What is the first of these numbers?
不同的质因数
首次出现连续两个数均有两个不同的质因数是在：
\[14 = 2 \times 7\] \[15 = 3 \times 5\]
首次出现连续三个数均有三个不同的质因数是在：
\[644 = 2^2 \times 7 \times 23\] \[645 = 3 \times 5 \times 43\] \[646 = 2 \times 17 \times 19\]
首次出现连续四个数均有四个不同的质因数时，其中的第一个数是多少？
我们可以获取数字的质因数组成的列表然后求交集进行判断：
(defun eu47-pfactor (n)
(let ((res))
(when (= (% n 2) 0)
(push 2 res)
(while (= (% n 2) 0)
(setq n (/ n 2))))
(named-let f ((i 3))
(cond
((> i n))
(t (if (= (% n i) 0)
(progn
(push i res)
(while (= (% n i) 0)
(setq n (/ n i)))
(f (+ i 2)))
(f (+ i 2))))))
res))
(cl-loop
for i from 1
with counter = 0
if (= (eu47-pfactor i) 3)
do (cl-incf counter)
else do (setq counter 0) end
if (= counter 3)
return (- i 3))
=> 134043