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Mathematics of Computation

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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: 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?)

    F. Behrend, “Über ’numeri abundantes.’ II,” Preuss. Akad. Wiss. Sitzungsber., v. 6, 1933, pp. 280-293. H. Davenport, “Über ’numeri abundantes,’ “ Preuss. Akad. Wiss. Sitzungsber., v. 26/29, 1933, pp. 830-837. 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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Keywords: Density, sum of divisors, arithmetic functions
Article copyright: © Copyright 1972 American Mathematical Society