On sums of the small divisors of a natural number

2019/10/25 by Douglas E. Iannucci, Iannucci, Douglas E.
Mathematics · #11A25 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11A25

paper · pdf · doi:10.48550/arxiv.1910.11835

12 pages. One figure

arxiv created 2019/10/25 · arxiv updated 2019/10/28

Abstract

We consider the positive divisors of a natural number that do not exceed its square root, to which we refer as the \it small divisors\/ of the natural number. We determine the asymptotic behavior of the arithmetic function that adds the small divisors of a natural number, and we consider its Dirichlet generating series.

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