Counting Heronian triangles based on area to perimeter ratios

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For Heronian triangles t with the perimeter p and area a, there are five distinct triangles with the area equal to the perimeter:

If a=p, count(t) = 5, if a=2p, count(t)=18.

For the area being an integer multiple of the perimeter, what is the sequence given by count(t), ie starting 5,18,...

source: Numberphile video 12min 43sec

https://www.youtube.com/watch?v=UIjeCKPHbso