Geodesic
On the distribution of $(k,r)$-integers in Piatetski-Shapiro sequences
Czechoslovak Mathematical Journal, Tome 71 (2021) no. 4, pp. 1063-1070
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A natural number $n$ is said to be a $(k,r)$-integer if $n=a^kb$, where $k>r>1$ and $b$ is not divisible by the $r$th power of any prime. We study the distribution of such $(k,r)$-integers in the Piatetski-Shapiro sequence $\{\lfloor n^c \rfloor \}$ with $c>1$. As a corollary, we also obtain similar results for semi-$r$-free integers.
A natural number $n$ is said to be a $(k,r)$-integer if $n=a^kb$, where $k>r>1$ and $b$ is not divisible by the $r$th power of any prime. We study the distribution of such $(k,r)$-integers in the Piatetski-Shapiro sequence $\{\lfloor n^c \rfloor \}$ with $c>1$. As a corollary, we also obtain similar results for semi-$r$-free integers.
DOI : 10.21136/CMJ.2021.0194-20
Classification : 11L07, 11N37
Keywords: $(k, r)$-integer; Piatetski-Shapiro sequence 
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Srichan, Teerapat. On the distribution of $(k,r)$-integers  in Piatetski-Shapiro sequences. Czechoslovak Mathematical Journal, Tome 71 (2021) no. 4, pp. 1063-1070. doi: 10.21136/CMJ.2021.0194-20

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