On the Sum and Product of Distinct Prime Factors of an Odd Perfect Number

2010/08/06 by Anirudh Prabhu, Prabhu, Anirudh
Mathematics · #Advanced Mathematical Theories #Analytic Number Theory Research #math.NT

paper · pdf · doi:10.48550/arxiv.1008.1114

arxiv created 2010/08/06 · arxiv updated 2010/08/09

Abstract

We present lower bounds on the sum and product of the distinct prime factors of an odd perfect number, which provide a lower bound on the size of the odd perfect number as a function of the number of its distinct prime factors.

Citations

• Finiteness of the Odd Perfect and Primitive Abundant Numbers with n Distinct Prime Factors

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• Bounds On Factors Of Odd Perfect Numbers
• 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
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