Aimin Guo

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math.NT2026

Exceptional sets for compositions involving Euler's function,the divisor-sum function and Dedekind's function

Aimin Guo

Let $ψ(n)$, $ϕ(n)$, and $σ(n)$ denote Dedekind's arithmetic function, Euler's totient function, and the sum-of-divisors function, respectively. We study exceptional sets asso…

math.NT2026

On the distribution of $ϕ (ψ (n))$ and $ψ (ψ (n))$

Aimin Guo

Let $ψ (n)$ and $ϕ (n)$ denote Dedekind's arithmetic function and Euler's totient function, respectively. We study the distribution of the compositions $ϕ (ψ (n))$ and $ψ (ψ (n))$ . In pa…

math.NT2025

On the Composition of the Euler Function and the Dedekind Arithmetic Function

Aimin Guo, Huan Liu, Qiyu Yang

Let $I (n) = \frac{ψ ( ϕ ( n ))}{ϕ ( ψ ( n ))}$ and $K (n) = \frac{ψ ( ϕ ( n ))}{ϕ ( ϕ ( n ))}$ , where $ϕ (n)$ is Euler's function and $ψ (n)$ is Dedekind's arithmetic function. We obtain the maximal orde…

Exceptional sets for compositions involving Euler's function,the divisor-sum function and Dedekind's function

On the distribution of ϕ(ψ(n)) and ψ(ψ(n))

On the Composition of the Euler Function and the Dedekind Arithmetic Function

On the distribution of $ϕ (ψ (n))$ and $ψ (ψ (n))$