On integers not of the form n - φ (n)
Volume 68 / 1995
Colloquium Mathematicum 68 (1995), 55-58
DOI: 10.4064/cm-68-1-55-58
Abstract
W. Sierpiński asked in 1959 (see [4], pp. 200-201, cf. [2]) whether there exist infinitely many positive integers not of the form n - φ(n), where φ is the Euler function. We answer this question in the affirmative by proving Theorem. None of the numbers $2^k·509203$ (k = 1, 2,...) is of the form n - φ(n).
