COUNTING INTEGERS WITH A SMOOTH TOTIENT

William D. Banks, John Friedlander, Carl Pomerance, Igor E. Shparlinski

Type: Article

Publication Date: 2019-09-10

Citations: 1

DOI: https://doi.org/10.1093/qmathj/haz026

Abstract

Abstract In an earlier paper we considered the distribution of integers $n$ for which Euler’s totient function at $n$ has all small prime factors. Here we obtain an improvement that is likely to be best possible.

Locations

arXiv (Cornell University) - View - PDF
The Quarterly Journal of Mathematics - View

Similar Works

Action	Title	Year	Authors
+	Counting integers with a smooth totient	2018	William D. Banks John Friedlander Carl Pomerance Igor E. Shparlinski
+	A Generalisation of Euler Totient Function	2022	Vlad Robu
+	Integers with a large smooth divisor	2006	William D. Banks Igor E. Shparlinski
+ PDF Chat	Integers with a Large Smooth Divisor	2007	William D. Banks Igor E. Shparlinski
+	Grimm's conjecture and smooth numbers	2012	Shanta Laishram M. Ram Murty
+	Counting primes revisited	2016	Alejandro Miralles Damià Torres
+	Arbitrarily tight bounds on the distribution of smooth integers	2002	DJ Daniel Bernstein
+	Approximating the Number of Prime Factors Given an Oracle to Euler's Totient Function.	2021	Yang Du Ilya Volkovich
+	Distribution of $αn + β$ modulo 1 over integers free from large and small primes	2017	Kam Hung Yau
+ PDF Chat	Sparse subsets of the natural numbers and Euler’s totient function	2019	Mithun Kumar Das Pramod Eyyunni Bhuwanesh Rao Patil
+	Distribution of $\alpha n + \beta$ modulo 1 over integers free from large and small primes	2017	Kam Hung Yau
+ PDF Chat	The Distribution of Smooth Numbers in Arithmetic Progressions	1992	Antal Balog Carl Pomerance
+	Divisibility of the central binomial coefficient $\binom {2n}{n}$	2020	Kevin Ford Sergeĭ Konyagin
+ PDF Chat	An Exact Formula for the Prime Counting Function	2019	Jose Risomar Sousa
+ PDF Chat	Residue classes free of values of Euler’s function	1999	Kevin Ford Sergeĭ Konyagin Carl Pomerance
+	On the Lehmer's problem involving Euler's totient function	2017	Huan Xiao
+	The Turán-Kubilius inequality for integers without large prime factors.	1982	Krishnaswami Alladi
+	Residue classes free of values of Euler's function	2020	Kevin R. Ford Sergeĭ Konyagin Carl Pomerance
+	Integers with many prime factors in diophantinely smooth sequences	1977	I. K�tai
+ PDF Chat	The Euler characteristic of Out($F_n$)	2020	Michael Borinsky Karen Vogtmann

Works That Cite This (1)

Action	Title	Year	Authors
+	Some thoughts on pseudoprimes	2021	Carl Pomerance Samuel S. Wagstaff

Works Cited by This (11)

Action	Title	Year	Authors
+ PDF Chat	Smooth Orders and Cryptographic Applications	2002	Carl Pomerance Igor E. Shparlinski
+	On the number of positive integers ≦ x and free of prime factors > y	1986	Adolf Hildebrand
+	ON THE NORMAL NUMBER OF PRIME FACTORS OF <i>p</i>-1 AND SOME RELATED PROBLEMS CONCERNING EULER'S ø-FUNCTION	1935	P. Erdős
+ PDF Chat	Smooth Values of the Iterates of the Euler Phi-Function	2007	Youness Lamzouri
+	Square values of Euler's function	2014	Paul Pollack Carl Pomerance
+ PDF Chat	Integers without large prime factors	1993	Adolf Hildebrand Gérald Tenenbaum
+	On The Number of Positive Integers ≤ x and Free of Prime Factors > y	1951	N.G. de Bruijn
+	On Amicable Numbers	2015	Carl Pomerance
+ PDF Chat	A note on square totients	2015	Tristan Freiberg Carl Pomerance
+	Popular subsets for Euler’s $$\varphi $$-function	2019	Paul Pollack