On the composition of the Euler function and the sum of divisors function
Jean-Marie De Koninck, Florian Luca (2007)
Colloquium Mathematicae
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Let H(n) = σ(ϕ(n))/ϕ(σ(n)), where ϕ(n) is Euler's function and σ(n) stands for the sum of the positive divisors of n. We obtain the maximal and minimal orders of H(n) as well as its average order, and we also prove two density theorems. In particular, we answer a question raised by Golomb.