The divisor function at consecutive integers

How can we establish the events {d(n) =d(n+1)} for infinitely many {n}?

https://londmathsoc.onlinelibrary.wiley.com/doi/abs/10.1112/S0025579300010743

Theorem: There are infinitely many integers {n} for which {d(n)=d(n+1)}. Indeed, for large {x}, the number of such {n \leqslant x} is at least of order {x(\log x)^{-7}}.

https://academic.oup.com/imrn/article-abstract/2011/7/1439/687263?redirectedFrom=fulltext

\displaystyle \#\{n \leqq x:(d(n), n)=1\}=c_{d} x+0\left(\sqrt{x}(\log x)^{3}\right) https://projecteuclid.org/download/pdf_1/euclid.rmjm/1250126920

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