47-smooth triangular numbers

 Published on Sunday, 11th December 2016, 07:00 am; Solved by 778;
Difficulty rating: 30%

Problem 581

A number is p-smooth if it has no prime factors larger than p.
Let T be the sequence of triangular numbers, ie T(n)=n(n+1)/2.
Find the sum of all indices n such that T(n) is 47-smooth.