A NEW SERIES FOR THE DENSITY OF ABUNDANT NUMBERS-Reference-Cited by-同舟云学术

A NEW SERIES FOR THE DENSITY OF ABUNDANT NUMBERS

Published:2014-01-22 Issue:01 Volume:10 Page:73-84
ISSN:1793-0421
Container-title:International Journal of Number Theory
language:en
Short-container-title:Int. J. Number Theory

Author:

KOBAYASHI MITSUO¹

Affiliation:

1. Department of Mathematics and Statistics, Cal Poly Pomona, 3801 West Temple Avenue, Pomona, CA 91768, USA

Abstract

A natural number n is called abundant if the sum of proper divisors of n exceeds n. In 1933 Behrend determined bounds for the natural density d𝒜 of abundant numbers, with subsequent improvements leading to the 1998 bounds of Deléglise, 0.2474 < d𝒜 < 0.2480. We present a new infinite series expression for the density of abundant numbers which can be used to calculate an improved lower bound.

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S1793042113500814

Reference12 articles.

1. On the distribution of primitive abundant numbers

2. E. Bessel-Hagen, Repertorium der Höheren Mathematik 1, ed. E. Pascal (Leipzig, Berlin, 1929) pp. 1458–1574.

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