# Upper bounds on the second largest prime factor of an odd perfect number

@article{Zelinsky2019UpperBO,
title={Upper bounds on the second largest prime factor of an odd perfect number},
author={Joshua Zelinsky},
journal={International Journal of Number Theory},
year={2019}
}
• Joshua Zelinsky
• Published 28 October 2018
• Mathematics
• International Journal of Number Theory
Acquaah and Konyagin showed that if [Formula: see text] is an odd perfect number with prime factorization [Formula: see text], where [Formula: see text], then one must have [Formula: see text]. Using methods similar to theirs, we show that [Formula: see text] and that [Formula: see text] We also show that if [Formula: see text] and [Formula: see text] are close to each other, then these bounds can be further strengthened.
3 Citations
On the small prime factors of a non-deficient number
Let $\sigma(n)$ to be the sum of the positive divisors of $n$. A number is non-deficient if $\sigma(n) \geq 2n$. We establish new lower bounds for the number of distinct prime factors of an odd
On the third largest prime divisor of an odd perfect number
• Mathematics
• 2019
Let $N$ be an odd perfect number and let $a$ be its third largest prime divisor, $b$ be the second largest prime divisor, and $c$ be its largest prime divisor. We discuss steps towards obtaining a
ON ODD PERFECT NUMBERS
In this note, we introduce the notion of the disc induced by an arithmetic function and apply this notion to the odd perfect number problem. We show that under certain special local condition an odd