Consecutive Squarefrees, Not Coprime

[Jud McCranie]

At 01:50 PM 8/20/2005, Leroy Quet wrote:
>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?

With a quick and dirty program, I get

174,422,474,602,831,843,930,1074,1182,1322,1374,1443,1518,1623,1803,
1974,2006,2022,2222,2274,2298,2522,2526,2595,2694,2870,2874,3122,3210,
3282,3423,3478,3574,3702,3770,3774,4022,4074,4202,4323,4359,4458,4474

It is A77395.