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Carmichael numbers composed of primes from a Beatty sequence

William D. Banks, Aaron M. Yeager (2011)

Colloquium Mathematicae

Let α,β ∈ ℝ be fixed with α > 1, and suppose that α is irrational and of finite type. We show that there are infinitely many Carmichael numbers composed solely of primes from the non-homogeneous Beatty sequence $ℬ_{α, β} = {(⌊ α n + β ⌋)}_{n = 1}^{\infty}$ . We conjecture that the same result holds true when α is an irrational number of infinite type.

Chen's theorem in short intervals

Ying Chun Cai, Ming Gao Lu (1999)

Acta Arithmetica

Coincidences in the values of the Euler and Carmichael functions

William D. Banks, John B. Friedlander, Florian Luca, Francesco Pappalardi, Igor E. Shparlinski (2006)

Acta Arithmetica

Comportement Moyen du Cardinal de Certains Ensembles de Facteurs Premiers.

Jacques Grah (1994)

Monatshefte für Mathematik

Composite positive integers whose sum of prime factors is prime

Florian Luca, Damon Moodley (2020)

Archivum Mathematicum

In this note, we show that the counting function of the number of composite positive integers $n \leq x$ such that $β (n) = \sum_{p ∣ n} p$ is a prime is of order of magnitude at least $x / {(log x)}^{3}$ and at most $x / log x$ .

Displaying 1 – 8 of 8

Carmichael numbers composed of primes from a Beatty sequence

Chen's theorem in short intervals

Coincidences in the values of the Euler and Carmichael functions

Comportement Moyen du Cardinal de Certains Ensembles de Facteurs Premiers.

Composite positive integers whose sum of prime factors is prime

Conditional bounds for small prime solutions of linear equations.

Correction au travail "Sur la densité de certains ensembles de multiples, 1", (Acta Arith. 69 (1995), 121-152)

Correction to the paper: On the sum-of-Divisors Function of the numbers of Fermat and Ferentinou-Nicolacopoulou

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