2018-10-10 22:03:03 +00:00
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---
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id: 5900f46b1000cf542c50ff7d
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2020-12-16 07:37:30 +00:00
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title: 问题254:数字因子的总和
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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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2021-01-13 02:31:00 +00:00
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dashedName: problem-254-sums-of-digit-factorials
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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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将f(n)定义为n的数字的阶乘的总和。例如,f(342)= 3! + 4! + 2! = 32。
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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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将sf(n)定义为f(n)的数字之和。所以sf(342)= 3 + 2 = 5。
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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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将g(i)定义为最小的正整数n,使得sf(n)= i。虽然sf(342)是5,但sf(25)也是5,并且可以证实g(5)是25。
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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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将sg(i)定义为g(i)的数字之和。所以sg(5)= 2 + 5 = 7。
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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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此外,可以证实g(20)是267并且1≤i≤20的Σsg(i)是156。
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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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什么是Σsg(i)1≤i≤150?
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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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`euler254()`应该返回8184523820510。
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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(euler254(), 8184523820510);
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2018-10-10 22:03:03 +00:00
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```
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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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# --seed--
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## --seed-contents--
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```js
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function euler254() {
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return true;
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}
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euler254();
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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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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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