arXiv subjects

Cody S. Hansen

Publications and source records attributed to Cody S. Hansen.

2 recordsLinked to original sources

arXiv2023

On inequalities involving counts of the prime factors of an odd perfect number

Let $N$ be an odd perfect number. Let $ω(N)$ be the number of distinct prime factors of $N$ and let $Ω(N)$ be the total number (counting multiplicity) of prime factors of $N$. We prove that $\frac{99}{37}ω(N) - \frac{187}{37} \leq Ω(N)$ and that if $3\nmid N$, then $\frac{51}{19}ω(N)-\frac{46}{19} \leq Ω(N)$.

math.NT↗

arXiv2022

Prime factors of $Φ_3(x)$ of the same form

We parameterize solutions to the equality $Φ_3(x)=Φ_3(a_1)Φ_3(a_2)\cdotsΦ_3(a_n)$ when each $Φ_3(a_i)$ is prime. Our focus is on the special cases when $n=2,3,4$, as this analysis simplifies and extends bounds on the total number of prime factors of an odd perfect number.

math.NT↗