---
id: 5900f4e61000cf542c50fff9
title: 'Problem 378: Triangle Triples'
challengeType: 5
forumTopicId: 302040
dashedName: problem-378-triangle-triples
---

# --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 &lt; j &lt; 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.

# --hints--

`euler378()` should return 147534623725724700.

```js
assert.strictEqual(euler378(), 147534623725724700);
```

# --seed--

## --seed-contents--

```js
function euler378() {

  return true;
}

euler378();
```

# --solutions--

```js
// solution required
```
