The density of squarefree numbers is well known.


I am wondering about the squarefree numbers in $[2,n]$ namely the second and higher moments of the gaps. Is anything known about these?



Gaps in Squarefree numbers
A number of authors e.g. Hooley, Filaseta, Trifonov have considered this problem of moments of gaps between square-free numbers. For example, [Filaseta and Trifonov](http://people.math.sc.edu/filaseta/papers/distribpaper.pdf) (paper in Proc. London Math. Soc. (1996); see Theorem 4) showed that for all $0\le \gamma < 43/13=3.30769\ldots$ one has 
$$ 
\sum\_{s\_{n+1}\le x} (s\_{n+1}-s\_n)^{\gamma} \sim B(\gamma) x, 
$$ 
for some constant $B(\gamma)$. Here $s\_n$ denotes the $n$-th square-free number. 


