2018-10-10 22:03:03 +00:00
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---
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id: 5900f5231000cf542c510035
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2020-12-16 07:37:30 +00:00
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title: 问题439:除数之和
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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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---
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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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令d(k)是k的所有除数之和。
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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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我们定义函数S(N)= ∑1≤i≤N ∑1≤j≤Nd(i·j)。
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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,S(3)= d(1)+ d(2)+ d(3)+ d(2)+ d(4)+ d(6)+ d(3)+ d(6)+ d( 9)= 59。
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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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给出S(103)= 563576517282和S(105)mod 109 = 215766508。 找出S(1011)mod 109。
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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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`euler439()`应该返回968697378。
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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(euler439(), 968697378);
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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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# --solutions--
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2020-08-13 15:24:35 +00:00
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