Skip to Main Content

Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Odd perfect numbers, Diophantine equations, and upper bounds
HTML articles powered by AMS MathViewer

by Pace P. Nielsen PDF
Math. Comp. 84 (2015), 2549-2567 Request permission


We obtain a new upper bound for odd multiperfect numbers. If $N$ is an odd perfect number with $k$ distinct prime divisors and $P$ is its largest prime divisor, we find as a corollary that $10^{12}P^{2}N<2^{4^{k}}$. Using this new bound, and extensive computations, we derive the inequality $k\geq 10$.
Similar Articles
  • Retrieve articles in Mathematics of Computation with MSC (2010): 11N25, 11Y50
  • Retrieve articles in all journals with MSC (2010): 11N25, 11Y50
Additional Information
  • Pace P. Nielsen
  • Affiliation: Department of Mathematics, Brigham Young University, Provo, Utah 84602
  • MR Author ID: 709329
  • Email:
  • Received by editor(s): June 14, 2013
  • Received by editor(s) in revised form: December 16, 2013
  • Published electronically: February 18, 2015
  • © Copyright 2015 American Mathematical Society
  • Journal: Math. Comp. 84 (2015), 2549-2567
  • MSC (2010): Primary 11N25; Secondary 11Y50
  • DOI:
  • MathSciNet review: 3356038