Geodesic
Squarefree numbers in the sequence $[\alpha n]$
Čebyševskij sbornik, Tome 14 (2013) no. 3, pp. 42-48

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An asymptotic formula for the number of squarefree integers of the form $[\alpha n]$ is proved in the paper, where $\alpha$ is an algebraic number or a number with restricted partial quotients.
Keywords: squarefree numbers, Beatty sequence, asymptotic formula, exponential sums. 
@article{CHEB_2013_14_3_a4,
     author = {D. V. Goryashin},
     title = {Squarefree numbers in the sequence $[\alpha n]$},
     journal = {\v{C}eby\v{s}evskij sbornik},
     pages = {42--48},
     publisher = {mathdoc},
     volume = {14},
     number = {3},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHEB_2013_14_3_a4/}
}
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D. V. Goryashin. Squarefree numbers in the sequence $[\alpha n]$. Čebyševskij sbornik, Tome 14 (2013) no. 3, pp. 42-48. http://geodesic.mathdoc.fr/item/CHEB_2013_14_3_a4/