Browsing General by Author "Cohen, Graeme"

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Browsing General by Author "Cohen, Graeme"

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  • Cohen, Graeme; Tonkes, Elliot (NJ Calkin & HS Wilf, 2001)
    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 ...
  • Cohen, Graeme; Iannucci, Douglas (University of Waterloo, Ontario, Canada, 2003)
  • Cohen, Graeme; Sorli, Ronald (Amer Mathematical Soc, 2010)
    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). ...
  • Iannucci, Douglas; Moujie, Deng; Cohen, Graeme (University of Waterloo, Ontario, Canada, 2003)
  • Cohen, Graeme (Amer Mathematical Soc, 2008)
    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 ...