Consecutive coincidences of Euler’s function-Reference-Cited by-同舟云学术

Consecutive coincidences of Euler’s function

Published:2016-04-10 Issue:04 Volume:12 Page:1011-1026
ISSN:1793-0421
Container-title:International Journal of Number Theory
language:en
Short-container-title:Int. J. Number Theory

Author:

Bayless Jonathan¹,Kinlaw Paul¹

Affiliation:

1. Department of Mathematics, Husson University, 1 College Circle, Bangor, ME 04401, USA

Abstract

We prove a version of the Hardy–Ramanujan inequality and a bound on the count of smooth numbers up to some number [Formula: see text], both with explicit constants. We use these as tools to prove a few interesting results on the values [Formula: see text] satisfying [Formula: see text] and provide an explicit bound on the sum of the reciprocals of such [Formula: see text].

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S1793042116500639

Reference16 articles.

1. Shifted primes without large prime factors

2. Reciprocal Sums as a Knowledge Metric: Theory, Computation, and Perfect Numbers

3. Analytic Number Theory

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