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

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 $1\le i<j<k\le n$ and $dT(i)>dT(j)>dT(k)$.
$Tr(20)=14$, $Tr(100)=5772$, and $Tr(1000)=11174776$.

Find $Tr(60000000)$.
Give the last 18 digits of your answer.