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isolated square free numberDefinitio

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An ``isolated square-free number'' is a square-free number 'q' which 'q-1' and 'q+1' are not square-free.
All the prime numbers are square-free, but not all of these are  as 'q'. The first 'q' is '17'. Let Q(x) be the cardinality of 'q' for 1$\leq q \leq x$, so e.g. $Q(100)=6$, i.e. 17,26,51,53 (twin 'q'!),91 and 97. Notice that $Q(100)< \text{than the twin primes in this interval}$. It is obvious from this definition give arises a lot of questions (and conjectures!). A claiming for these special numbers was requested at