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A generalization of the Euler's totient function [PDF]

Asian-European Journal of Mathematics, 2015
The main goal of this paper is to provide a group theoretical generalization of the well-known Euler’s totient function. This determines an interesting class of finite groups.
I. Cuza
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On a generalization of the Euler totient function

Functiones et Approximatio Commentarii Mathematici, 2021
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Sets of monotonicity for Euler’s totient function

The Ramanujan Journal, 2012
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Pollack, Paul, Pomerance, Carl, Treviño, Enrique   +2 more
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Deterministic Integer Factorization with Oracles for Euler’s Totient Function

Fundamenta Informaticae, 2020
In this paper, we construct deterministic factorization algorithms for natural numbers N under the assumption that the prime power decomposition of Euler’s totient function φ( N) is known. Their runtime complexities depend on the number ω( N) of distinct prime divisors of N, and we present efficient methods for relatively small ...
Markus Hittmeir, Jacek Pomykala
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A Probabilistic Look at Series Involving Euler's Totient Function

Integers, 2012
Abstract.We use a probabilistic method to evaluate the limit ...
Yung-Pin Chen
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Chapter VI Euler's Totient Function and the Theorem of Euler

, 1988

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Two remarks on iterates of Euler’s totient function

Archiv der Mathematik, 2011
Let \(\varphi_k\) denote the \(k\)th iterate of Euler's \(\varphi\) function. In this paper, the author determines the average values of \(\varphi_k\) and \(1/\varphi_k\). That is, he shows that for each \(k\geq 0\), one has \[ {{1}\over {x}}\sum_{n\leq x} \varphi_k (n)\sim {{3}\over {k!e^{k\gamma}\pi^2}} {{x^2}\over {(\log\log\log x)^k}} \] as \(x\to ...
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Totient Functions on the Euler Number Tree

1993
In [4], we defined three kinds of number tree, and described some of their properties. The third kind we called the Regular Knot Tree (RKT), and showed how it arose as a law of evolution of the string-runs of Regular Knots (which are a type of cylindrical braid).
J. C. Turner, H. Garcia, A. G. Schaake
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p-Adic Valuation of Euler’s Totient Function

Bulletin of the Malaysian Mathematical Sciences Society
Let \(\phi(n)\) be the Euler phi function. The paper proves theorems about what powers of primes can divide \(\phi(n)\) and how large those prime powers can be. Let \(v_p(n)\) be the largest number \(k\) such that \(p^k|n\). Then they note that trivially one has that \(v_2(\phi(n)) \leq \lfloor \log_2 n\rfloor\).
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New Problem For Euler’s Totient Function

In 1932, D. H. Lehmer asked if there are any composite numbers n such that phit(n)/ n-1. where phi(n) the Euler totient function, is defined as the number of positive integers \leq n that are relatively prime to n. In this paper, we study other problem of appropriate of Euler totient function phi(n), with n are odd composite numbers, such that if m<
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