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CONSECUTIVE SQUARE-FREE NUMBERS IN PIATETSKI-SHAPIRO SEQUENCES

Part of: Multiplicative number theory

Published online by Cambridge University Press:  13 September 2021

PINTHIRA TANGSUPPHATHAWAT Open the ORCID record for PINTHIRA TANGSUPPHATHAWAT [Opens in a new window] ,
TEERAPAT SRICHAN Open the ORCID record for TEERAPAT SRICHAN [Opens in a new window]  and
VICHIAN LAOHAKOSOL Open the ORCID record for VICHIAN LAOHAKOSOL [Opens in a new window]
PINTHIRA TANGSUPPHATHAWAT
Affiliation:
Department of Mathematics, Faculty of Science and Technology, Phranakhon Rajabhat University, Bangkok10220, Thailand e-mail: [email protected]
TEERAPAT SRICHAN*
Affiliation:
Department of Mathematics, Faculty of Science, Kasetsart University, Bangkok10900, Thailand
VICHIAN LAOHAKOSOL
Affiliation:
Department of Mathematics, Faculty of Science, Kasetsart University, Bangkok10900, Thailand e-mail: [email protected]
*
e-mail: [email protected]
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Abstract

Using a method due to Rieger [‘Remark on a paper of Stux concerning squarefree numbers in non-linear sequences’, Pacific J. Math.78(1) (1978), 241–242], we prove that the Piatetski-Shapiro sequence defined by $\{\lfloor n^c \rfloor : n\in \mathbb {N}\}$ contains infinitely many consecutive square-free integers whenever $1<c<3/2$ .

Keywords

Piatetski-Shapiro sequencesquare-free number

MSC classification

Primary: 11N64: Other results on the distribution of values or the characterization of arithmetic functions
Secondary: 11N37: Asymptotic results on arithmetic functions
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 105 , Issue 2 , April 2022 , pp. 217 - 222
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Copyright
© 2021 Australian Mathematical Publishing Association Inc.

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