• Corpus ID: 31396476


  author={Theodore M. Porter},
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 succeed. But is there a formula? Are there infinitely many? In the first millennium of the common era, Thâbit ibn Qurra came close with a formula for a subfamily of amicable pairs, but it is far from clear that his formula gives infinitely many examples and probably it does not. A special case of… 

Can the Various Meanings of Probability Be Reconciled

The stand-off between the frequentist and subjectivist interpretations of probability has hardened into a philosophy. According to this philosophy, probability begins as pure mathematics. The

Mutual Influence between Different Views of Probability and Statistical Inference

In this paper, we analyse the various meanings of probability and its different applications, and we focus especially on the classical, the frequentist, and the subjectivist view. We describe the

Number ecologies: numbers and numbering practices

In putting together this Special Issue we seek to contribute to the social study of number, a field which has acquired renewed significance in recent years with a revival in forms of selfand

Quetelet and the emergence of the behavioral sciences

Astronomer and statistician, Adolphe Quetelet sought to apply the mathematical tools of astronomy to create was called a ‘mathematics of society’, and demonstrated regularities in the incidence of various social phenomena, notably crime.

History of mathematics: some thoughts about the general situation

I consider the situation in the history of probability and statistics which is almost the same, as I presume, in the history of mathematics and perhaps in the history of science in general. The main

Whatever happened to reversion?

Constructing public statistics : the history of the Argentine cost of living index, 1918-1943

Statistics contribute to the understanding of events by objectifying phenomena, as they are perceived to reflect or be an approximation of reality. This perception is based on the premise that

A Historical and Philosophical Perspective on Probability

This chapter presents a twenty first century historical and philosophical perspective on probability, related to the teaching of probability. It is important to remember the historical development as

The Anatomy of Credulity and Incredulity: Or, a Hermeneutics of Misinformation

This essay explores the historical process by which the birth and expansion of information systems transformed the relationship between “faith” and “fact.” The existence of recurring forms of

Statistical Practice: Putting Society on Display

As a contribution to current debates on the ‘social life of methods’, in this article we present an ethnomethodological study of the role of understanding within statistical practice. After reviewing



On Primitive Abundant Numbers

Let vn be an integer and denote by A'@) the sum of its divisors. Let The number W. is called a primitive nbunda.nt number (say p.a.n.) if u(m) 3 2, but, for ajm, u(a) < 2. Primit'ive abundant numbers

Common values of the arithmetic functions ϕ and σ

We show that the equation ϕ(a) = σ(b) has infinitely many solutions, where ϕ is Euler's totient function and σ is the sum‐of‐divisors function. This proves a fifty‐year‐old conjecture of Erdős.

On the density of abundant numbers

This paper considers results on the computational complexity of the algorithm used by Deléglise as well as recent improvements to the algorithm which allow us to discover the next decimal digit.

On the Normal Behavior of the Iterates Of some Arithmetic Functions

Let ϕ1(n) = ϕ(n) where ϕ is Euler’s function, let ϕ2(n) = ϕ(ϕ(n)), etc. We prove several theorems about the normal order of ϕk(n) and state some open problems. In particular, we show that the normal

Two contradictory conjectures concerning Carmichael numbers

Preliminary conjectures are derived that are consistent with Shanks's observations, while fitting in with the viewpoint of Erdos and the results of Alford, Granville and Pomerance.

The Distribution of Totients

AbstractThis paper is a comprehensive study of the set of totients, i.e., the set of values taken by Euler's φ-function. The main functions studied are V(x), the number of totients ≤x, A(m), the

Sieving by very thin sets of primes, and Pratt trees with missing primes

Suppose P is a set of primes, such that for every p in P, every prime factor of p-1 is also in P. If P does not contain all primes, we apply a new sieve method to show that the counting function of P

Bounds for the Density of Abundant Integers

It is said that an integer n is abundant if the sum of the divisors of n is at least 2n and the set of abundant numbers has a natural density A(2) and the sharper bounds are given.