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Amicable numbers and their connection to the Euler totient function

open access: yes
A pair of numbers is amicable if each number equals the sum of the proper divisors of the other. This paper after exploring the history and evolution of amicable numbers, introduces a novel characterization of amicable pairs whose greatest common divisor is a power of two, using their distinct prime factorizations. Specifically, we examine pairs of the
Mavaddat, Ali Reza, Alikhani, Saeid
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A note on Euler’s totient function [PDF]

open access: yesNotes on Number Theory and Discrete Mathematics, 2019
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