Unitary analogues of a generalized number-theoretic sum
2
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
In this paper, we investigate the sums of the elements in the finite set $\{x^{k}:1\leq x\leq\frac{n}{m},\gcd_u(x,n)=1\}$, where $k$, $m$ and $n$ are positive integers and $\gcd_u(x,n)$ is the unitary greatest common divisor of $x$ and $n$. Moreover, for some cases of $k$ and $m$, we can give the explicit formulae for the sums involving some well-known arithmetic functions.
Abstract
In this paper, we investigate the sums of the elements in the finite set $\{x^{k}:1\leq x\leq\frac{n}{m},\gcd_u(x,n)=1\}$, where $k$, $m$ and $n$ are positive integers and $\gcd_u(x,n)$ is the unitary greatest common divisor of $x$ and $n$. Moreover, for some cases of $k$ and $m$, we can give the explicit formulae for the sums involving some well-known arithmetic functions.
참고문헌 (8)
- J. D. Baum, "A number-theoretic sum", Math. Mag, 55(2), pp.111~113 (1982)[DOI]
- D. M. Burton, "Elementary Number Theory" (2011), McGraw-Hill
- E. Cohen, "Arithmetical functions associated with the unitary divisors of an integer", Math. Z, 74, pp.66~80 (1960)[DOI]
- Narakorn Rompurk Kanasri, "Generalizations of number-theoretic sums", 대한수학회논문집, 34(4), pp.1105~1115 (2019), 대한수학회[DOI]
- N. R. Kanasri, "A simple proof of generalizations of number-theoretic sums", Songklanakarin J. Sci. Technol, 44(2), pp.450~458 (2022)[DOI]
- K. Nageswara Rao, "On the unitary analogues of certain totients", Monatsh. Math, 70, pp.149~154 (1966)[DOI]
- I. Niven, "An Introduction to the Theory of Numbers" (1991), John Wiley & Sons, Inc
- R. Sivaramakrishnan, "Classical theory of arithmetic functions, Monographs and Textbooks in Pure and Applied Mathematics, 126" (1989), Marcel Dekker, Inc.