# Associate Professor Graeme Cohen

**Associate of the Faculty,**School of Mathematical Sciences

Ph. D

**Phone**

+61 2 9514 2257

**Fax**

+61 2 9514 2260

**Room**

CB01.15.61

## Books

Cohen, G.L. 2006,

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*Counting Australia In - People, Organisations and Institutions of Australian Mathematics*, 1, Halstead Press, Sydney, Australia.View/Download from: UTSePress

## Conference Papers

Cohen, G.L. 2004, 'A new statistic in cricket - the slog factor', Australasian Conference on Mathematics and Computers in Sport, Palmerston, New Zealand, August 2004 in

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*Proceedings of the Seventh Australasian Conference on Mathematics and Computers in Sport*, ed Mortin, R.H.; Ganesalingam, S., Massey University, New Zealand, pp. 127-132.View/Download from: UTSePress

Clowes, S., Cohen, G.L. & Tomljanovic, L. 2002, 'Dynamic evaluation of conditional probabilities of winning a tennis match', Sixth Australian Conference on Mathematics and Computers in Sport, Gold Coast, Australia, July 2002 in

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*Proceedings of the Sixth Australian Conference on Mathematics and Computers in Sport*, ed Cohen G; Langtry T, UTS, Sydney, pp. 112-118.View/Download from: UTSePress

Cohen, G.L. 2002, 'Cricketing Chances', Sixth Australian Conference on Mathematics and Computers in Sport, Gold Coast, Australia, July 2002 in

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*Proceedings of the Sixth Australian Conference on Mathematics and Computers in Sport*, ed Cohen G; Langtry T, UTS, Sydney, pp. Jan-13-NA.View/Download from: UTSePress

## Journal Articles

Cohen, G.L. & Sorli, R.M. 2010, 'Odd Harmonic Numbers Exceed 1024',

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*Mathematics Of Computation*, vol. 79, no. 272, pp. 2451-2460.View/Download from: UTSePress | Publisher's site

A number n > 1 is harmonic if sigma(n) vertical bar n tau(n), where tau(n) and sigma(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 10(16). We show here that, for any odd

Cohen, G.L. 2008, 'Superharmonic Numbers',

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*Mathematics Of Computation*, vol. 78, no. 265, pp. 421-429.View/Download from: UTSePress | Publisher's site

Let tau(n) denote the number of positive divisors of a natural number n > 1 and let sigma( n) denote their sum. Then n is superharmonic if sigma(n) vertical bar n(k)tau(n) for some positive integer k. We deduce numerous properties of superharmonic numbers and show in particular that the set of all superharmonic numbers is the first nontrivial example that has been given of an infinite set that contains all perfect numbers but for which it is difficult to determine whether there is an odd member.

Cohen, G.L. & Iannucci, D.E. 2003, 'Derived sequences',

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*Journal of Integer Sequences*, vol. 6, no. 1, pp. 1-9.View/Download from: UTSePress

Iannucci, D.E., Moujie, D. & Cohen, G.L. 2003, 'On perfect totient numbers',

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*Journal of Integer Sequences*, vol. 6, no. 1, pp. 1-7.View/Download from: UTSePress

Cohen, G.L. & Sorli, R.M. 2003, 'On the number of distinct prime factors of an odd perfect number',

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*Journal of Discrete Algorithms*, vol. 1, pp. 21-35.View/Download from: UTSePress | Publisher's site

Cohen, G.L. 2002, 'Three cusion biliards: notes on the diamond system',

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*Sports Engineering*, vol. 5, no. N/A, pp. 43-51.View/Download from: UTSePress | Publisher's site

Cohen, G.L. 2002, 'On a theorem of GH Hardy concerning golf',

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*Mathematical Gazette*, vol. 86, no. N/A, pp. 120-125.View/Download from: UTSePress

de Mestre, N. & Cohen, G.L. 2002, 'Land and water speed records',

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*Sports Engineering*, vol. 5, no. N/A, pp. 207-212.View/Download from: UTSePress

Cohen, G.L. & Tonkes, E. 2001, 'Dartboard Arrangements',

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*Electronic Journal of Combinatorics*, vol. 8, no. 2, pp. 1-8.View/Download from: UTSePress

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 penalty cost function and a string reversal algorithm is used to determine all arrangements that maximise the penalty, for any p 1. The maximum value of the penalty function for p = 1 is well known in the literature, and has been previously stated without proof for p = 2. We determine it also for p = 3 and p = 4.

Moujie, D. & Cohen, G.L. 2000, 'A Note on a Conjecture of Jesmanowicz',

*Colloquium Mathematicum*, vol. 86, no. 1, pp. 25-30.