Erdős, Paul Some remarks on Euler’s \(\varphi\)-function and some related problems. (English) Zbl 0061.08005 Bull. Am. Math. Soc. 51, 540-544 (1945). The following is part of a joint review for six articles on the Euler \(\varphi\)-function:Using Brun’s method the author proves, that if \(N\geq 3\), the number of integers \(n\) not exceeding \(N\), for which the equation \(\varphi(x)=n\) is solvable, is greater than a positive constant times \(N(\log N)^{-1}\log\log N\). Reviewer: P. T. Bateman Page: −5 −4 −3 −2 −1 ±0 +1 +3 +4 +5 Show Scanned Page Cited in 1 ReviewCited in 15 Documents MSC: 11A25 Arithmetic functions; related numbers; inversion formulas Keywords:Euler function PDFBibTeX XMLCite \textit{P. Erdős}, Bull. Am. Math. Soc. 51, 540--544 (1945; Zbl 0061.08005) Full Text: DOI Online Encyclopedia of Integer Sequences: Decimal expansion of zeta(2)*zeta(3)/zeta(6). Decimal expansion of lim_{i->oo} c(i)/i, where c(i) is the number of integers k such that sigma(k) < i (A074753).