Corpus ID: 14818194

# Divisibility by 3 of even multiperfect numbers of abundancy 3 and 4

```@inproceedings{Broughan2010DivisibilityB3,
title={Divisibility by 3 of even multiperfect numbers of abundancy 3 and 4},
author={K. Broughan and Q. Zhou},
year={2010}
}```
• Published 2010
• Mathematics
We say a number is flat if it can be written as a non-trivial power of 2 times an odd squarefree number. The power is the “exponent” and the number of odd primes the “length”. Let N be flat and 4-perfect with exponent a and length m. If a 6≡ 1 mod 12, then a is even. If a is even and 3 ∤ N then m is also even. If a ≡ 1 mod 12 then 3 | N and m is even. If N is flat and 3-perfect and 3 ∤ N, then if a 6≡ 1 mod 12, a is even. If a ≡ 1 mod 12 then m is odd. If N is flat and 3 or 4-perfect then it is… Expand
2 Citations
On Odd Perfect Numbers and Even 3-Perfect Numbers
• Mathematics, Computer Science
• Integers
• 2012
Abstract. An idea used in the characterization of even perfect numbers is used, first, to derive new necessary conditions for the existence of an odd perfect number and, second, to show that thereExpand
Note on the Theory of Perfect Numbers
A perfect number is a number whose divisors add up to twice the number itself. The existence of odd perfect numbers is a millennia-old unsolved problem. This note proposes a proof of the nonexistenceExpand