---
id: 5900f4e61000cf542c50fff9
challengeType: 5
title: 'Problem 378: Triangle Triples'
---

## Description
<section id='description'>
Let T(n) be the nth triangle number, so T(n) =


n (n+1)2

.


Let dT(n) be the number of divisors of T(n).
E.g.:
T(7) = 28 and dT(7) = 6.


Let Tr(n) be the number of triples (i, j, k) such that 1 ≤ i < j < k ≤ n and dT(i) > dT(j) > dT(k).
Tr(20) = 14, Tr(100) = 5772 and Tr(1000) = 11174776.


Find Tr(60 000 000).
Give the last 18 digits of your answer.
</section>

## Instructions
<section id='instructions'>

</section>

## Tests
<section id='tests'>

```yml
tests:
  - text: <code>euler378()</code> should return 147534623725724700.
    testString: assert.strictEqual(euler378(), 147534623725724700, '<code>euler378()</code> should return 147534623725724700.');

```

</section>

## Challenge Seed
<section id='challengeSeed'>

<div id='js-seed'>

```js
function euler378() {
  // Good luck!
  return true;
}

euler378();
```

</div>



</section>

## Solution
<section id='solution'>

```js
// solution required
```
</section>