Explicit bounds for large gaps between squarefree integers

Abstract

We obtain explicit forms of the current best known asymptotic upper bounds for gaps between squarefree integers. In particular we show, for any $x\ge 2$, that every interval of the form $(x,x+11x^{1/5}\log x]$ contains a squarefree integer. The constant 11 can be improved further, if $x$ is assumed to be larger than a (very) large constant.