Andreas J. Weingartner

activity

20102020

collaborators

6 papers

math.NT2020

An extension of the Siegel-Walfisz theorem

Andreas Weingartner

We extend the Siegel-Walfisz theorem to a family of integer sequences that are characterized by constraints on the size of the prime factors. Besides prime powers, this family incl…

math.NT2020

On primes and practical numbers

Carl Pomerance, Andreas Weingartner

A number $n$ is practical if every integer in $[1, n]$ can be expressed as a subset sum of the positive divisors of $n$ . We consider the distribution of practical numbers that are a…

math.NT2019

The constant factor in the asymptotic for practical numbers

Andreas Weingartner

An integer $n \geq 1$ is said to be practical if every natural number $m \leq n$ can be expressed as a sum of distinct positive divisors of $n$ . The number of practical numbers up to…

math.CO2018

Set partitions without blocks of certain sizes

Joshua Culver, Andreas Weingartner

We give an asymptotic estimate for the number of partitions of a set of $n$ elements, whose block sizes avoid a given set $S$ of natural numbers. As an application, we de…

math.NT2016

A sieve problem and its application

Andreas Weingartner

Let $θ$ be an arithmetic function and let $B$ be the set of positive integers $n = p_{1}^{α_{1}} \dots p_{k}^{α_{k}}$ , which satisfy $p_{j+1} \le θ( p_1^{α_1}\cdots p_{j}^{α_{j}})…

math.NT2010

The distribution functions of $σ (n) / n$ and $n / ϕ (n)$ , II

Andreas Weingartner

Let $σ (n)$ be the sum of the positive divisors of $n$ , and let $A (t)$ be the natural density of the set of positive integers $n$ satisfying $σ (n) / n \geq t$ . We give an improved asym…

An extension of the Siegel-Walfisz theorem

On primes and practical numbers

The constant factor in the asymptotic for practical numbers

Set partitions without blocks of certain sizes

A sieve problem and its application

The distribution functions of σ(n)/n and n/ϕ(n), II

The distribution functions of $σ (n) / n$ and $n / ϕ (n)$ , II