A search procedure and lower bound for odd perfect numbers-Reference-Cited by-同舟云学术

A search procedure and lower bound for odd perfect numbers

Published:1973 Issue:124 Volume:27 Page:943-949
ISSN:0025-5718
Container-title:Mathematics of Computation
language:en
Short-container-title:Math. Comp.

Author:

Tuckerman Bryant

Abstract

An infinite tree-generating "q-algorithm" is defined, which if executed would enumerate all odd perfect numbers (opn’s). A truncated execution shows that any opn has either some component p a > 10 18 {p^a} > {10^{18}} , with a even, or no divisor > 7 > 7 ; hence any opn must be > 10 36 > {10^{36}} .

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,Computational Mathematics,Algebra and Number Theory

Link

http://www.ams.org/mcom/1973-27-124/S0025-5718-1973-0325506-7/S0025-5718-1973-0325506-7.pdf

Reference9 articles.

1. Odd perfect numbers;McCarthy, Paul J.;Scripta Math.,1957

2. Über mehrfach vollkommene Zahlen. II;Kanold, Hans-Joachim;J. Reine Angew. Math.,1957

3. Remarks on the number of factors of an odd perfect number;Norton, Karl K.;Acta Arith.,1960

4. On divisors of odd perfect numbers;Muskat, Joseph B.;Math. Comp.,1966

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1. A NEW LOWER BOUND FOR ODD PERFECT NUMBERS;MATH COMPUT;1989

2. On the largest component of an odd perfect number;Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics;1987-04

3. Some recent results of number theory discovered with electronic computers;International Journal of Mathematical Education in Science and Technology;1982-09

4. Divisibility;Unsolved Problems in Number Theory;1981

5. LOWER BOUND FOR SET OF ODD PERFECT NUMBERS;MATH COMPUT;1973