Dynamics of a function related to the primes

被引：0

作者：

Ying Shi

Quanhui Yang

机构：

[1] Nanjing University of Traditional Chinese Medicine,Department of Mathematics

[2] Nanjing University of Information Science and Technology,School of Mathematics and Statistics

来源：

Chinese Annals of Mathematics, Series B | 2015年 / 36卷

关键词：

Dynamics; The largest prime factor; Arithmetic function; 11A41; 37B99;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

Let n = p1p2 ⋯ pk, where pi (1 ≤ i ≤ k) are primes in the descending order and are not all equal. Let Ωk(n) = P(p1+p2)P(p2+p3) ⋯ P(pk−1+pk)P(pk +p1), where P(n) is the largest prime factor of n. Define w0(n) = n and wi(n) = w(wi−1(n)) for all integers i ≥ 1. The smallest integer s for which there exists a positive integer t such that Ωks(n) = Ωks+t(n) is called the index of periodicity of n. The authors investigate the index of periodicity of n.

引用

页码：81 / 90

页数：9

共 10 条

[1] Chen Y G(2008)Dynamics of the Proc. Amer. Math. Soc. 136 2351-2357
[2] Shi Y(2008) function and the Green-Tao theorem on arithmetic progressions in the primes J. Number Theory 128 2085-2090
[3] Chen Y G(2012)Distribution of primes and dynamics of the J. Number Theory 132 390-409
[4] Shi Y(2006) function J. Number Theory 119 86-98
[5] Chen Y G(2009)Dynamics of Golding’s Sci. in China Ser. A 52 849-856
[6] Shi Y(2008)-function J. Math. Res. Exposition 28 886-890
[7] Wu J(undefined)Dynamics of the undefined undefined undefined-undefined
[8] Goldring W(undefined) function and primes undefined undefined undefined-undefined
[9] Jia C H(undefined)On the inverse problem relative to dynamics of the undefined undefined undefined-undefined
[10] Shi Y(undefined) function undefined undefined undefined-undefined

← 1 →