• Corpus ID: 116974690

Solving the Odd Perfect Number Problem: Some Old and New Approaches

@article{Dris2012SolvingTO,
title={Solving the Odd Perfect Number Problem: Some Old and New Approaches},
author={Jose Arnaldo B. Dris},
journal={arXiv: Number Theory},
year={2012}
}

More on the total number of prime factors of an odd perfect number

• K. Hare
• Mathematics
Math. Comput.
• 2005
This paper extends results to show that n is perfect if a(n) = 2n and defines the total number of prime factors of N as Ω(N):= a + 2Σ k j=1 β j .

The second largest prime divisor of an odd perfect number exceeds ten thousand

The latter bound of the statement in the title of this paper is improved, showing that the largest prime divisor of an odd perfect number must exceed 10 6 , and Hagis showed that the second largest must exceeds 10 3 .

On the total number of prime factors of an odd perfect number

• Mathematics
Math. Comput.
• 2003
It is proved that if βj ≡ 1 (mod 3) orβj ≡ 2 (mod 5) for all j, 1 ≤ j ≤ k, then 3|n is perfect, where σ(n) denotes the sum of the positive divisors of n.

On the Largest Prime Divisor of an Odd Perfect Number

• Mathematics
• 1973
It is shown here that if n is odd and perfect, then n has a prime divisor which exceeds 11200. 0. In 1944 Kanold (2) showed that at least one of the /?, is greater than or equal to 61. Our purpose

PERFECT NUMBERS: AN ELEMENTARY INTRODUCTION

This serves as an elementary introduction to the history and theory surrounding even perfect numbers. One would be hard put to find a set of whole numbers with a more fascinating history and more

The third largest prime divisor of an odd perfect number exceeds one hundred

It is proved that the third largest prime divisor of an odd perfect number must exceed 100.

Improved techniques for lower bounds for odd perfect numbers

• Computer Science
• 1989
It is proved here that, subject to certain conditions verifiable in polynomial time, in fact N > q5k/2, and the computations in an earlier paper are extended to show that N > 10300.