Consecutive Squarefrees, Not Coprime

[Leroy Quet]

I feel like an idiot for asking this question, whose solution must be 
obvious.

Is this sequence in the EIS? (It *must* be.)

Sequence: the lowest of 2 consecutive square-free integers, m and n, 
where m and n are not coprime.

I think the sequence begins 174, ...
(because 177 is the next squarefree integer, and both 174 and 177 are 
divisible by 3.)

I do not believe there are any others <= 500, unless I overlooked 
something.

If this sequence is not in the EIS (which would be a surprise), could 
someone please calculate/submit it?

thanks,
Leroy Quet