School of Mathematical Sciences

Globalization and advances in communications technology, notably satellite television and broadband internet, have greatly expanded the potential marketplace for professional sport teams. As a resu...

Background: Lifethreatening illnesses in young people are traumatic for patients and their families. Support services can help patients and families deal with various nonmedical impacts of diagno...

Let τ(n) denote the number of positive divisors of a natural number n > 1 and let σ(n) denote their sum. Then n is superharmonic if σ(n)  nκτ(n) for some positive integer κ. We deduce numerous pro...

A number n > 1 is harmonic if σ(n) σ nτ(n), where τ(n) and σ(n) are the number of positive divisors of n and their sum, respectively. It is known that there are no odd harmonic numbers up to 1015. ...


This note considers possible arrangements of the sectors of a generalised dartboard. The sum of the pth powers of the absolute differences of the numbers on adjacent sectors is introduced as a pena...

Let n > 2 be a positive integer and let φ denote Euler's totient function. Define φ1(n) = φ(n) and φk(n) = φ(φk1(n)) for all integers k ≥ 2. Define the arithmetic function S by S(n) = φ(n) + φ2(n)...

We say n ∈ ℕ is perfect if σ (n) = 2n, where σ(n) denotes the sum of the positive divisors of n. No odd perfect numbers are known, but it is well known that if such a number exists, it must have pr...

We define a multiplicative arithmetic function D by assigning D(p a) = apa1, when p is a prime and a is a positive integer, and, for n ≥ 1, we set D0(n) = n and Dk(n) = D(D k1(n)) when k ≥ 1. We ...

© 2014 IEEE. Pointing is a typical means of directing a human's attention to a specific object or event. Robot pointing behaviours that direct the attention of humans are critical for humanrobot i...