Number of prime divisors of \(\varphi_ k(n)\), where \(\varphi_ k\) is the \(k\)-fold iterative of \(\varphi\)

DOI10.1006/jnth.1997.2164zbMath0878.11036OpenAlexW2050631933MaRDI QIDQ1363095

Imre Kátai, M. Wijsmuller, Nader L. Bassily

Publication date: 17 August 1997

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jnth.1997.2164

zbMATH Keywords

sieve methodsEuler's totient functionGaussian limit lawBombieri additive functionsTurán-Kubilius inequality Erdös-Kac theorem

Mathematics Subject Classification ID

Asymptotic results on arithmetic functions (11N37) Applications of sieve methods (11N36) Arithmetic functions; related numbers; inversion formulas (11A25) Arithmetic functions in probabilistic number theory (11K65)

Related Items (3)

Prime chains and Pratt trees ⋮ Two remarks on iterates of Euler's totient function ⋮ On the equations ϕ(n) = ϕ(n + k) and ϕ(p − 1) = ϕ(q − 1)

Cites Work

• An analogue of the Erdős-Kac theorem for Fourier coefficients of modular forms
• On the number of prime factors of \(\varphi{} (\varphi{}(n))\)
• On the normal number of prime factors of \(\phi(n)\)
• On the large sieve
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