I started thinking about triangle numbers recently. Specifically, multiples of Triangle numbers. Are there any triangle numbers that when multiplied to a positive integer other than 1 (or 0) give another triangle number? Aside from the obvious fact that 1 is a triangle number and you can multiply that with another triangle to get the same triangle out, what else is there? And what are the properties of these numbers?

Examples off the top of my head:

2*3 = 6

6*6 = 36

12*10 = 120

3*15 = 45

5*21 = 105

Strange.

Infinitely many. t(n) = n(n+1)/2

for example t(6) = (6)(7)/2 = 21 and t(2) = (2)(3)/2 = 3

21 = 7(3)

so t(6) = 7*t(2)

Another one: t(8) = 6*t(3)

Or: t(15) = 12*t(4)