Eric,
T(6) = 112 (not 122). Nice sequences.
I was surprised to find that the first few terms 1, 2, 3, 8, 10, 16, 21
comprising the denominators in D = {1/1, 6/2, 21/3, 32/8, 60/10, 112/16,
189/21} match A060697, but otherwise there seems to be no relation.
Ed Jeffery