On the small prime factors of a non-deficient number

2020/05/25 by Zelinsky, Joshua · 1 citation
#11A25 #11N64 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2005.12118

Abstract

Let σ(n) to be the sum of the positive divisors of n. A number is non-deficient if σ(n) ≥ 2n. We establish new lower bounds for the number of distinct prime factors of an odd non-deficient number in terms of its second smallest, third smallest and fourth smallest prime factors. We also obtain tighter bounds for odd perfect numbers. We also discuss the behavior of σ(n!+1), σ(2ⁿ+1), and related sequences.

Cited by

• On near superperfect numbers, the Goormaghtigh conjecture, and Mertens' theorem

Related

• New techniques for bounds on the total number of Prime Factors of an Odd Perfect Number
• The sum of the reciprocals of the prime divisors of an odd perfect or odd primitive non-deficient number
• On odd deficient-perfect numbers with four distinct prime divisors
• On the Sum and Product of Distinct Prime Factors of an Odd Perfect Number
• On Exactly 3-Deficient-Perfect Numbers