Before we talk about what I did, let talk briefly about the basic idea of the inequalities going into O result. You may have seen before that Sigma(n), the sum of all the positive divisors of an integer n is a multiplicative function. This is a good exercise if one hasn seen it (caution! when a number theorist says that a function f(n) is multiplicative they don mean that f(ab)=f(a)f(b) for all integers a and b.
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