# 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, Counting Australia In - People, Organisations and Institutions of Australian Mathematics, 1, Halstead Press, Sydney, Australia.

## 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 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.
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 Proceedings of the Sixth Australian Conference on Mathematics and Computers in Sport, ed Cohen G; Langtry T, UTS, Sydney, pp. 112-118.
Cohen, G.L. 2002, 'Cricketing Chances', Sixth Australian Conference on Mathematics and Computers in Sport, Gold Coast, Australia, July 2002 in Proceedings of the Sixth Australian Conference on Mathematics and Computers in Sport, ed Cohen G; Langtry T, UTS, Sydney, pp. Jan-13-NA.

## Journal Articles

Cohen, G.L. & Sorli, R.M. 2010, 'Odd Harmonic Numbers Exceed 1024', Mathematics Of Computation, vol. 79, no. 272, pp. 2451-2460.
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', Mathematics Of Computation, vol. 78, no. 265, pp. 421-429.
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', Journal of Integer Sequences, vol. 6, no. 1, pp. 1-9.
Iannucci, D.E., Moujie, D. & Cohen, G.L. 2003, 'On perfect totient numbers', Journal of Integer Sequences, vol. 6, no. 1, pp. 1-7.