2018-10-10 22:03:03 +00:00
|
|
|
|
---
|
|
|
|
|
id: 5900f3b11000cf542c50fec4
|
2020-12-16 07:37:30 +00:00
|
|
|
|
title: 问题69大欧拉
|
2018-10-10 22:03:03 +00:00
|
|
|
|
challengeType: 5
|
|
|
|
|
videoUrl: ''
|
2021-01-13 02:31:00 +00:00
|
|
|
|
dashedName: problem-69-totient-maximum
|
2018-10-10 22:03:03 +00:00
|
|
|
|
---
|
|
|
|
|
|
2020-12-16 07:37:30 +00:00
|
|
|
|
# --description--
|
2018-10-10 22:03:03 +00:00
|
|
|
|
|
2020-12-16 07:37:30 +00:00
|
|
|
|
Euler的Totient函数φ(n)\[有时称为phi函数]用于确定小于n的数字的数量,这些数字是n的相对素数。例如,如1,2,4,5,7和8都小于9且相对于9,φ(9)= 6。
|
2018-10-10 22:03:03 +00:00
|
|
|
|
|
2020-12-16 07:37:30 +00:00
|
|
|
|
n相对素数φ(n)n /φ(n)2 1 1 2 3 1,2 2 1.5 4 1,3 2 2 5 1,2,3,4 4 1.25 6 1,5 2 3 7 1,2, 3,4,5,6 6 1.1666 ... 8 1,3,5,7 4 2 9 1,2,4,5,7,8 6 1.5 10 1,3,7,9 4 2.5
|
2018-10-10 22:03:03 +00:00
|
|
|
|
|
2020-12-16 07:37:30 +00:00
|
|
|
|
可以看出,对于n≤10,n = 6产生最大n /φ(n)。找到n≤1,000,000的值,其中n /φ(n)是最大值。
|
2018-10-10 22:03:03 +00:00
|
|
|
|
|
2020-12-16 07:37:30 +00:00
|
|
|
|
# --hints--
|
2018-10-10 22:03:03 +00:00
|
|
|
|
|
2020-12-16 07:37:30 +00:00
|
|
|
|
`euler69()`应该返回510510。
|
2018-10-10 22:03:03 +00:00
|
|
|
|
|
|
|
|
|
```js
|
2020-12-16 07:37:30 +00:00
|
|
|
|
assert.strictEqual(euler69(), 510510);
|
2018-10-10 22:03:03 +00:00
|
|
|
|
```
|
|
|
|
|
|
2021-01-13 02:31:00 +00:00
|
|
|
|
# --seed--
|
|
|
|
|
|
|
|
|
|
## --seed-contents--
|
|
|
|
|
|
|
|
|
|
```js
|
|
|
|
|
function totientMaximum() {
|
|
|
|
|
|
|
|
|
|
return true;
|
|
|
|
|
}
|
|
|
|
|
|
|
|
|
|
totientMaximum();
|
|
|
|
|
```
|
|
|
|
|
|
2020-12-16 07:37:30 +00:00
|
|
|
|
# --solutions--
|
2020-08-13 15:24:35 +00:00
|
|
|
|
|
2021-01-13 02:31:00 +00:00
|
|
|
|
```js
|
|
|
|
|
// solution required
|
|
|
|
|
```
|