The Forestry of Adversarial Totient Iterations
Abstract
We give a closed-form expression for (1+(2+(3+...+(n), where is Euler's totient function. More generally, for an integer sequence A=\aj\ we study the value of A(n)=(a1+(a2+(a3+...+(an) when A is the perfect squares or the perfect cubes. We show A(n) is bounded for all sequences considered. We also present the Arboreal Algorithm which can sometimes determine a closed form of A(n) using tree-like structures.
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