Shapiro, Harold An arithmetic function arising from the \(\varphi\)-function. (English) Zbl 0061.08002 Am. Math. Mon. 50, 18-30 (1943). The following is part of a joint review for six articles on the Euler \(\varphi\)-function:The author proves various elementary properties of the arithmetic function \(C(n)\), defined for positive integers \(n>2\)) as the unique positive integer \(k\) such that \(\varphi^k(n)=2\), where \(\varphi^k\) denotes the \(k\)-th iterate of \(\varphi\). Reviewer: P. T. Bateman Page: −5 −4 −3 −2 −1 ±0 +1 +3 +4 +5 Show Scanned Page Cited in 8 ReviewsCited in 9 Documents MSC: 11A25 Arithmetic functions; related numbers; inversion formulas Keywords:\(k\)-th iterate of Euler function PDFBibTeX XMLCite \textit{H. Shapiro}, Am. Math. Mon. 50, 18--30 (1943; Zbl 0061.08002) Full Text: DOI Online Encyclopedia of Integer Sequences: The n-th term is the sum of lengths of iteration chains to get fixed points(=1) for the Euler totient function from 1 to n. Numbers k such that A007755(k) is prime.