a2b2ef3f75
* fix: clean-up Project Euler 441-460 * fix: corrections from review Co-authored-by: Tom <20648924+moT01@users.noreply.github.com> Co-authored-by: Tom <20648924+moT01@users.noreply.github.com>
49 lines
1013 B
Markdown
49 lines
1013 B
Markdown
---
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id: 5900f5261000cf542c510038
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title: 'Problem 441: The inverse summation of coprime couples'
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challengeType: 5
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forumTopicId: 302113
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dashedName: problem-441-the-inverse-summation-of-coprime-couples
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---
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# --description--
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For an integer $M$, we define $R(M)$ as the sum of $\frac{1}{p·q}$ for all the integer pairs $p$ and $q$ which satisfy all of these conditions:
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- $1 ≤ p < q ≤ M$
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- $p + q ≥ M$
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- $p$ and $q$ are coprime.
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We also define $S(N)$ as the sum of $R(i)$ for $2 ≤ i ≤ N$.
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We can verify that $S(2) = R(2) = \frac{1}{2}$, $S(10) ≈ 6.9147$ and $S(100) ≈ 58.2962$.
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Find $S({10}^7)$. Give your answer rounded to four decimal places.
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# --hints--
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`inverseSummationCoprimeCouples()` should return `5000088.8395`.
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```js
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assert.strictEqual(inverseSummationCoprimeCouples(), 5000088.8395);
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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 inverseSummationCoprimeCouples() {
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return true;
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}
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inverseSummationCoprimeCouples();
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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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