Problem 44732. Highly divisible triangular number (inspired by Project Euler 12)

Triangular numbers can be calculated by the sum from 1 to n. For example, the first 10 triangular numbers are:

 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ...

All divisors for each of these numbers are listed below

 1: 1
 3: 1,3
 6: 1,2,3,6
 10: 1,2,5,10
 15: 1,3,5,15
 21: 1,3,7,21
 28: 1,2,4,7,14,28
 36: 1,2,3,4,6,9,12,18,36
 45: 1,3,5,9,15,45
 55: 1,5,11,55

Your challenge is to write a function that will return the value of the first triangular number to have over d divisors (d will be passed to your function).