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Estimating The Density Of The Abundant Numbers, Dominic Klyve, Melissa Pidde, Kathryn E. Temple
Estimating The Density Of The Abundant Numbers, Dominic Klyve, Melissa Pidde, Kathryn E. Temple
Mathematics Faculty Scholarship
Mathematicians have been interested in properties of abundant numbers – those which are smaller than the sum of their proper factors – for over 2,000 years. During the last century, one line of research has focused in particular on determining the density of abundant numbers in the integers. Current estimates have brought the upper and lower bounds on this density to within about 10−4, with a value of K ≈ 0.2476, but more precise values seem difficult to obtain. In this paper, we employ computational data and tools from inferential statistics to get more insight into this value. We also …