Consecutive Squarefrees, Not Coprime

[Jud McCranie]

At 09:09 PM 8/24/2005, Jud McCranie wrote:

>I've found that with high probability, a(6) = 9216772051242   (and its 
>partner is  9216772051254).  At this point I can't be sure that there 
>isn't a smaller one, but there probably isn't a smaller one.  Soon I hope 
>to have either a proof that it is the smallest (very likely it is) or 
>possibly find a smaller one.

Factorizations (from Maple):

                    (2)  (3)  (7)  (8841181)  (24821)


                            2
                        (41)   (283)  (19374241)


                           2
                        (2)   (239)  (9640974949)


                             2
               (3)  (5)  (11)   (19)  (29)  (179)  (51487)


                              2
                     (2)  (17)   (105871)  (150617)


                               2
                           (37)   (6732485063)


                         4     3
                      (2)   (3)   (6347849)  (3361)


                           3
                        (7)   (1187)  (22637789)


                              4
                      (2)  (5)   (212203)  (34747)


                                      2
                       (3)  (61)  (73)   (9451093)


                           2
                        (2)   (901131409)  (2557)


                                2
                      (13)  (67)   (421)  (375149)


                   (2)  (3)  (1669)  (12743)  (72227)