Problem 378
Triangle Triples

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 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.

These problems are part of Project Euler and are licensed under CC BY-NC-SA 2.0 UK

http://projecteuler.net/problem=378