47 lines
833 B
Markdown
47 lines
833 B
Markdown
---
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id: 5900f5231000cf542c510035
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title: 'Problem 439: Sum of sum of divisors'
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challengeType: 5
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forumTopicId: 302110
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dashedName: problem-439-sum-of-sum-of-divisors
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---
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# --description--
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Let $d(k)$ be the sum of all divisors of $k$.
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We define the function $S(N) = \sum_{i = 1}^N \sum_{j = 1}^N d(i \times j)$.
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For example, $S(3) = d(1) + d(2) + d(3) + d(2) + d(4) + d(6) + d(3) + d(6) + d(9) = 59$.
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You are given that $S({10}^3) = 563\\,576\\,517\\,282$ and $S({10}^5)\bmod {10}^9 = 215\\,766\\,508$.
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Find $S({10}^{11})\bmod {10}^9$.
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# --hints--
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`sumOfSumOfDivisors()` should return `968697378`.
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```js
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assert.strictEqual(sumOfSumOfDivisors(), 968697378);
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```
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# --seed--
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## --seed-contents--
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```js
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function sumOfSumOfDivisors() {
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return true;
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}
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sumOfSumOfDivisors();
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```
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# --solutions--
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```js
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// solution required
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```
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