On some variations of perfect and multiperfect numbers

A positive integer is said to be perfect if the sum of its divisors is twice the number. This paper is a partial exposition of the articles On Multiply Perfect Numbers with a Special Property by Carl Pomerance (1975), Variations on Euclid's Formula for Perfect Numbers by Farideh Firoozbakt (201...

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Main Authors: Quintana, Noel Enrico, Sancho, Miguel Antonio
Format: text
Language:English
Published: Animo Repository 2010
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Online Access:https://animorepository.dlsu.edu.ph/etd_bachelors/5334
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Institution: De La Salle University
Language: English
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spelling oai:animorepository.dlsu.edu.ph:etd_bachelors-57802021-04-16T03:05:51Z On some variations of perfect and multiperfect numbers Quintana, Noel Enrico Sancho, Miguel Antonio A positive integer is said to be perfect if the sum of its divisors is twice the number. This paper is a partial exposition of the articles On Multiply Perfect Numbers with a Special Property by Carl Pomerance (1975), Variations on Euclid's Formula for Perfect Numbers by Farideh Firoozbakt (2010), and Iterating the Sum-of-Divisors Function by Graeme Cohen and Herman te Riele. The paper deals with different variations of perfect numbers. The first major result determined solutions to a problem involving the sum-of-divisors function satisfying certain conditions. The results showed that all solutions are multiperfect numbers, a generalization of perfect numbers in which the sum of the divisors is a positive integral multiple of the number. The second article dealt with generalizing the concept of multiperfect numbers by iterating the sum-of-divisors function σ, giving rise to what we call (m,k)-perfect numbers. One of the questions that was attempted to e answered was Are all numbers (m,k)-perfect? It was shown that numbers up to 1000 are (m,k)-perfect. The third article gave solutions to various variations of Euclid's equation of the form σ(x), = kx + f(x), where k is an integer larger than 1 and f is an arithmetic function of x. 2010-01-01T08:00:00Z text https://animorepository.dlsu.edu.ph/etd_bachelors/5334 Bachelor's Theses English Animo Repository Perfect numbers Mathematics
institution De La Salle University
building De La Salle University Library
continent Asia
country Philippines
Philippines
content_provider De La Salle University Library
collection DLSU Institutional Repository
language English
topic Perfect numbers
Mathematics
spellingShingle Perfect numbers
Mathematics
Quintana, Noel Enrico
Sancho, Miguel Antonio
On some variations of perfect and multiperfect numbers
description A positive integer is said to be perfect if the sum of its divisors is twice the number. This paper is a partial exposition of the articles On Multiply Perfect Numbers with a Special Property by Carl Pomerance (1975), Variations on Euclid's Formula for Perfect Numbers by Farideh Firoozbakt (2010), and Iterating the Sum-of-Divisors Function by Graeme Cohen and Herman te Riele. The paper deals with different variations of perfect numbers. The first major result determined solutions to a problem involving the sum-of-divisors function satisfying certain conditions. The results showed that all solutions are multiperfect numbers, a generalization of perfect numbers in which the sum of the divisors is a positive integral multiple of the number. The second article dealt with generalizing the concept of multiperfect numbers by iterating the sum-of-divisors function σ, giving rise to what we call (m,k)-perfect numbers. One of the questions that was attempted to e answered was Are all numbers (m,k)-perfect? It was shown that numbers up to 1000 are (m,k)-perfect. The third article gave solutions to various variations of Euclid's equation of the form σ(x), = kx + f(x), where k is an integer larger than 1 and f is an arithmetic function of x.
format text
author Quintana, Noel Enrico
Sancho, Miguel Antonio
author_facet Quintana, Noel Enrico
Sancho, Miguel Antonio
author_sort Quintana, Noel Enrico
title On some variations of perfect and multiperfect numbers
title_short On some variations of perfect and multiperfect numbers
title_full On some variations of perfect and multiperfect numbers
title_fullStr On some variations of perfect and multiperfect numbers
title_full_unstemmed On some variations of perfect and multiperfect numbers
title_sort on some variations of perfect and multiperfect numbers
publisher Animo Repository
publishDate 2010
url https://animorepository.dlsu.edu.ph/etd_bachelors/5334
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