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| Dynamics of a Function Related to the Primes |
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Citation： |
Ying SHI,Quanhui YANG.Dynamics of a Function Related to the Primes[J].Chinese Annals of Mathematics B,2015,36(1):81~90 |
| Page view： 1519
Net amount： 1222 |
Authors： |
Ying SHI; Quanhui YANG; |
Foundation： |
the National Natural Science Foundation of China (Nos. 11371195,
11471017), the Youth Foundation of Mathematical Tianyuan of China (No. 11126302) and the Project
of Graduate Education Innovation of Jiangsu Province (No.CXZZ12-0381). |
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| Abstract： |
Let $ n=p_{1}p_{2}\cdots p_{k}$, where $p_i~(1\le i\le k)$ are
primes in the descending order and are not all equal. Let $\Omega_k
(n)= P(p_{1}+ p_{2})P(p_{2}+ p_{3})\cdots
P(p_{k-1}+p_{k})P(p_{k}+p_{1})$, where $P(n)$ is the largest prime
factor of $n$. Define $w^{0}(n)=n$ and $w^{i}(n)=w(w^{i-1}(n))$ for
all integers $i\ge 1$. The smallest integer $s$ for which there
exists a positive integer $t$ such that
$\Omega_k^{s}(n)=\Omega_k^{s+t}(n)$ is called the index of
periodicity of $n$. The authors investigate the index of periodicity
of $n$. |
Keywords： |
Dynamics, The largest prime factor, Arithmetic function |
Classification： |
11A41, 37B99 |
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