Definition. 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$\le q\le x$, so e.g. $Q(100)=6$, i.e. 17,26,51,53 (twin ’q’!),91 and 97. Notice that $$. It is obvious from this definition give arises a lot of questions (and conjectures!). A claiming for these special numbers was requested at OEIS.org.

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## Comments

## I forgot the number 19.

## isolated square free numbers

I prefer the definition as follows: prime numbers and composite numbers in which each prime factor occurs only with exponent equal to one. Examples of such composites: 6, 35, 65, 93….

## isolated square free numbers

I prefer the definition as follows: prime numbers and composite numbers in which each prime factor occurs only with exponent equal to one. Examples of such composites: 6, 35, 65, 93….