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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Density bounds for the sum of divisors function


Authors: Charles R. Wall, Phillip L. Crews and Donald B. Johnson
Journal: Math. Comp. 26 (1972), 773-777
MSC: Primary 10H25; Secondary 10L10
Erratum: Math. Comp. 31 (1977), 616.
MathSciNet review: 0327700
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Abstract | References | Similar Articles | Additional Information

Abstract: Upper and lower bounds are presented for the density of the integers $ n$ for which $ \sigma (n)/n \geqq x$, where $ \sigma (n)$ is the sum of divisors of $ n$, and $ 1 \leqq x \leqq 5$.


References [Enhancements On Off] (What's this?)

  • [1] F. Behrend, ``Über 'numeri abundantes.' II,'' Preuss. Akad. Wiss. Sitzungsber., v. 6, 1933, pp. 280-293.
  • [2] H. Davenport, ``Über 'numeri abundantes,' `` Preuss. Akad. Wiss. Sitzungsber., v. 26/29, 1933, pp. 830-837.
  • [3] C. Wall, Topics Related to the Sum of Unitary Divisors of an Integer, Ph.D. Dissertation, University of Tennessee, Knoxville, Tenn., 1970.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1972-0327700-7
PII: S 0025-5718(1972)0327700-7
Keywords: Density, sum of divisors, arithmetic functions
Article copyright: © Copyright 1972 American Mathematical Society