Flammenkamp, A.; Luca, F. Infinite families of noncototients. (English) Zbl 0965.11003 Colloq. Math. 86, No. 1, 37-41 (2000). Let as usual \(\varphi\) denote Euler’s function. A positive integer \(n\) is called a noncototient, if the equation \(x- \varphi(x)= n\) has no solution \(x\). The conjecture of P. Erdős and W. Sierpiński, that there are infinitely many such numbers, was confirmed by J. Browkin and A. Schinzel [Colloq. Math. 68, 55-58 (1995; Zbl 0820.11003)] by showing that every integer of the form \(2^n\cdot k\) for \(k= 509203\) is a noncototient. In the present paper the authors give sufficient conditions on positive integers \(k\) with the same property. Further six other integers \(k\) are determined. Reviewer: Thomas Maxsein (Clausthal) Cited in 1 ReviewCited in 3 Documents MSC: 11A25 Arithmetic functions; related numbers; inversion formulas 11B25 Arithmetic progressions Keywords:Euler’s function; noncototient Citations:Zbl 0820.11003 PDFBibTeX XMLCite \textit{A. Flammenkamp} and \textit{F. Luca}, Colloq. Math. 86, No. 1, 37--41 (2000; Zbl 0965.11003) Full Text: DOI EuDML Online Encyclopedia of Integer Sequences: Noncototients: numbers k such that x - phi(x) = k has no solution. Prime Riesel numbers p that are not Mersenne primes such that 2*p is a noncototient.