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Iteration of the $$\varphi$$-function. (English) Zbl 0061.08003
The following is part of a joint review for six articles on the Euler $$\varphi$$-function:
By giving counter-examples the author refutes a conjecture of Shapiro that if $$k$$ is given, the least $$n$$ with $$C(n)=k$$ is prime [see H. S. Shapiro, Am. Math. Mon. 50, 18–30 (1943; Zbl 0061.08002)].
Reviewer: P. T. Bateman

##### MSC:
 11A25 Arithmetic functions; related numbers; inversion formulas
Euler function
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