School of Mathematical Sciences
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© 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 human-robot i...
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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. ...
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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...
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We define a multiplicative arithmetic function D by assigning D(p a) = apa-1, 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 k-1(n)) when k ≥ 1. We ...
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Background: Life-threatening illnesses in young people are traumatic for patients and their families. Support services can help patients and families deal with various non-medical impacts of diagno...
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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...
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Let n > 2 be a positive integer and let φ denote Euler's totient function. Define φ1(n) = φ(n) and φk(n) = φ(φk-1(n)) for all integers k ≥ 2. Define the arithmetic function S by S(n) = φ(n) + φ2(n)...
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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...
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Date issued
- 6 2010 - 2014
- 23 2001 - 2009
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Type
- 21 Journal Article
- 5 Conference Proceeding
- 1 Book
- 1 Chapter
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- 18 closed_access
- 11 open_access