Le Maohua, “On Mersenne Numbers” [in Chinese], Journal of Jishou University (Natural Science Edition) 20(1) (March 1999): 17–19, shows that the squarefree part of $2^p - 1$, with $p \ge 11$ prime, is greater than $(\pi{}p/log\thinspace{}p)^2$.
John Blythe Dobson
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