Integers with large practical component

2014/11/25 by Andreas Weingartner, Weingartner, Andreas
Mathematics · #11N25 #11N37 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11N25 #msc:11N37

paper · pdf · doi:10.48550/arxiv.1411.6974

8 pages; updated references; to appear in Publ. Math. Debrecen

arxiv created 2015/06/25 · arxiv updated 2015/06/26

Abstract

A positive integer n is called practical if all integers between 1 and n can be written as a sum of distinct divisors of n. We give an asymptotic estimate for the number of integers ≤ x which have a practical divisor ≥ y.

Related

• Practical numbers and the distribution of divisors
• A generalization of the practical numbers
• The constant factor in the asymptotic for practical numbers
• Practical pretenders
• On practical sets and A-practical numbers