Is there a specific terminology for numbers which are nontrivial multiples of triangular numbers?

Question

(Note: Please see this new question for the motivation.)

A number $T$ is said to be triangular if it could be written in the form $$T=\frac{n(n+1)}{2},$$ where $n$ is a positive integer.

Here is my question:

Is there a specific terminology for numbers which are nontrivial multiples of triangular numbers?

That is, is there a specific name for numbers $T'$ which are of the form $$T' = dT = d\cdot\bigg(\frac{n(n+1)}{2}\bigg),$$ for some integer $d > 1$?

I tried searching for the relevant sequence in OEIS, but all I am seeing are references to $T'$ being triangular as well.

Answer 1

I'm going to answer based on the confirmation in the comment.

• Note that if $T'>1$, then taking $d=T'$ and $n=1$ (so that $T=1*2/2=1$) works.
• Also, since $d>1$, $T'=1$ is impossible.
• And since $n,d\ge1$, $T'<1$ is impossible as well.

Therefore, a name for the possible values of $T'$ is "integers greater than 1".