The distribution of square-free numbers of the form [n c ]
Journal de théorie des nombres de Bordeaux, Tome 10 (1998) no. 2, pp. 287-299

It is proved that the sequence [n c ](n=1,2,⋯) contains infinite squarefree integers whenever 1<c<61 36=1.6944⋯, which improves Rieger’s earlier range 1<c<1.5.

Nous montrons que pour 1<c<61 36=1.6944⋯, la suite n c n=1,2,⋯ contient une infinité d’entiers sans facteur carré ; cela améliore un résultat antérieur dû à Rieger qui obtenait l’infinitude de ces entiers pour 1<c<1.5.

Keywords: square-free number, exponential sum, exponent pair 
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Xiaodong Cao; Wenguang Zhai. The distribution of square-free numbers of the form $[n^c]$. Journal de théorie des nombres de Bordeaux, Tome 10 (1998) no. 2, pp. 287-299. https://jtnb.centre-mersenne.org/item/JTNB_1998__10_2_287_0/

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