2018-10-10 22:03:03 +00:00
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---
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id: 5900f53d1000cf542c51004f
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2020-12-16 07:37:30 +00:00
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title: 问题464:莫比乌斯函数和区间
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2018-10-10 22:03:03 +00:00
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challengeType: 5
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videoUrl: ''
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2021-01-13 02:31:00 +00:00
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dashedName: problem-464-mbius-function-and-intervals
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2018-10-10 22:03:03 +00:00
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---
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2020-12-16 07:37:30 +00:00
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# --description--
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2018-10-10 22:03:03 +00:00
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2020-12-16 07:37:30 +00:00
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Möbius函数,表示为μ(n),定义为:μ(n)=( - 1)ω(n),如果n是无平方(其中ω(n)是n的不同素因子的数量)μ(n) )如果n不是无平方,则= 0。
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2018-10-10 22:03:03 +00:00
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2020-12-16 07:37:30 +00:00
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令P(a,b)为区间\[a,b]中的整数n,使得μ(n)= 1.设N(a,b)为区间\[a,b]中的整数n这样μ(n)= -1。例如,P(2,10)= 2且N(2,10)= 4。
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2018-10-10 22:03:03 +00:00
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2020-12-16 07:37:30 +00:00
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令C(n)为整数对(a,b)的数目,使得:1≤a≤b≤n,99·N(a,b)≤100·P(a,b),和99·P( a,b)≤100·N(a,b)。
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2018-10-10 22:03:03 +00:00
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2020-12-16 07:37:30 +00:00
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例如,C(10)= 13,C(500)= 16676和C(10000)= 20155319。
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2018-10-10 22:03:03 +00:00
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2020-12-16 07:37:30 +00:00
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找C(2 000 000)。
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2018-10-10 22:03:03 +00:00
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2020-12-16 07:37:30 +00:00
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# --hints--
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2018-10-10 22:03:03 +00:00
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2020-12-16 07:37:30 +00:00
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`euler464()`应返回198775297232878。
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2018-10-10 22:03:03 +00:00
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```js
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2020-12-16 07:37:30 +00:00
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assert.strictEqual(euler464(), 198775297232878);
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2018-10-10 22:03:03 +00:00
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```
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2021-01-13 02:31:00 +00:00
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# --seed--
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## --seed-contents--
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```js
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function euler464() {
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return true;
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}
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euler464();
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```
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2020-12-16 07:37:30 +00:00
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# --solutions--
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2020-08-13 15:24:35 +00:00
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2021-01-13 02:31:00 +00:00
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```js
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// solution required
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```
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