47 lines
914 B
Markdown
47 lines
914 B
Markdown
---
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id: 5900f5191000cf542c51002c
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title: 'Problem 429: Sum of squares of unitary divisors'
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challengeType: 5
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forumTopicId: 302099
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dashedName: problem-429-sum-of-squares-of-unitary-divisors
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---
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# --description--
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A unitary divisor $d$ of a number $n$ is a divisor of $n$ that has the property $gcd(d, \frac{n}{d}) = 1$.
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The unitary divisors of $4! = 24$ are 1, 3, 8 and 24.
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The sum of their squares is $12 + 32 + 82 + 242 = 650$.
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Let $S(n)$ represent the sum of the squares of the unitary divisors of $n$. Thus $S(4!) = 650$.
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Find $S(100\\,000\\,000!)$ modulo $1\\,000\\,000\\,009$.
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# --hints--
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`sumSquaresOfUnitaryDivisors()` should return `98792821`.
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```js
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assert.strictEqual(sumSquaresOfUnitaryDivisors(), 98792821);
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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 sumSquaresOfUnitaryDivisors() {
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return true;
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}
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sumSquaresOfUnitaryDivisors();
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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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