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A set of Good Numbers

Source: 2018 Korea Winter Program Practice Test 1 #7

February 1, 2018
number theory

Problem Statement

Let nn be a "Good Number" if sum of all divisors of nn is less than 2n2n for n∈Z.n\in \mathbb{Z}. Does there exist an infinite set MM that satisfies the following?
For all a,b∈M,a,b\in M, a+ba+b is good number. (a=ba=b is allowed.)
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