DISTRIBUTION OF r-FREE INTEGERS OVER A FLOOR FUNCTION SET

被引：0
|
作者：
Tangsupphathawat, Pinthira [1 ]
Srichan, Teerapat [2 ]
Laohakosol, Vichian [2 ]
机构：
[1] Phranakhon Rajabhat Univ, Fac Sci & Technol, Bangkok 10220, Thailand
[2] Kasetsart Univ, Fac Sci, Bangkok 10900, Thailand
来源：
BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY | 2023年 / 108卷 / 01期
关键词：
floor function; r-free integer; MULTIPLICATIVE FUNCTIONS; NUMBERS;
D O I：
10.1017/S0004972722001241
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
For a positive integer $r\geq 2$, a natural number n is r-free if there is no prime p such that $p<^>r\mid n$. Asymptotic formulae for the distribution of r-free integers in the floor function set $S(x):=\{\lfloor x/ n \rfloor :1\leq n\leq x\}$ are derived. The first formula uses an estimate for elements of $S(x)$ belonging to arithmetic progressions. The other, more refined, formula makes use of an exponent pair and the Riemann hypothesis.
引用
收藏
页码：107 / 113
页数：7
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