Zur Dichte der Menge der vollkommenen Zahlen

  title={Zur Dichte der Menge der vollkommenen Zahlen},
  author={Bernhard Hornfeck},
  journal={Archiv der Mathematik},

Paul Erdős and the Rise of Statistical Thinking in Elementary Number Theory

It might be argued that elementary number theory began with Pythagoras who noted two-and-a-half millennia ago that 220 and 284 form an amicable pair. That is, if s(n) denotes the sum of the proper

Rationally almost periodic sequences, polynomial multiple recurrence and symbolic dynamics

A set $R\subset \mathbb{N}$ is called rational if it is well approximable by finite unions of arithmetic progressions, meaning that for every $\unicode[STIX]{x1D716}>0$ there exists a set $B=\bigcup

Reciprocal Sums as a Knowledge Metric: Theory, Computation, and Perfect Numbers

A new use for reciprocal sums is introduced; that is, they can be used as a knowledge metric to classify the current state of number theorists’ understanding of a given class of integers.


When faced with remarkable examples such as this it is natural to wonder how special they are. Through the centuries mathematicians tried to find other examples of amicable pairs, and they did indeed

The First Years

Wie kann man Primzahlen erkennen

Dass die Aufgabe, die Primzahlen von den zusammengesetzten zu unterscheiden und letztere in ihre Primfactoren zu zerlegen, zu den wichtigsten und nutzlichsten der gesamten Arithmetik gehort und die

How to Recognize Whether a Natural Number is a Prime

The problem of distinguishing prime numbers from composite numbers and of resolving the latter into their prime factors is known to be one of the most important and useful in arithmetic.

Über die Häufigkeit vollkommener Zahlen

Decatizing apparatus comprises a steaming cylinder and a suction cylinder. Respective primary backing cloths are associated with the steaming and suction cylinders to press the fabric to be treated



On the density of some sequences of numbers

The fun&ions f(m) and 4(m) are called additive and multiplicative respectively if they are defined for non-negative integers m, and if, for (ml, m,) = 1, fhm,) =f(W+fhL In my paper " On the density