--description--

Let $T(n)$ be the $n^{\text{th}}$ triangle number, so $T(n) = \frac{n(n + 1)}{2}$.

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 $dT(i) > dT(j) > dT(k)$. $Tr(20) = 14$, $Tr(100) = 5\,772$ and $Tr(1000) = 11\,174\,776$.

Find $Tr(60\,000\,000)$. Give the last 18 digits of your answer.

--hints--

triangleTriples() should return 147534623725724700.

assert.strictEqual(triangleTriples(), 147534623725724700);

--seed--

--seed-contents--

function triangleTriples() {

  return true;
}

triangleTriples();

--solutions--

// solution required