Generalising ‘Sums of cubes equal to squares of sums’

  title={Generalising ‘Sums of cubes equal to squares of sums’},
  author={J. Mason},
  journal={The Mathematical Gazette},
  • J. Mason
  • Published 2001
  • Mathematics
  • The Mathematical Gazette
  • David Pagni drew attention to a result which is ascribed by Dickson [2, p. 286] to Liouville (1857), that the sum of the cubes of the number of divisors of each of the divisors of an integer, is equal to the square of their sum. For example, the divisors of 6 are 1, 2, 3, and 6, which have 1, 2, 2, and 4 divisors respectively, and Pagni observed, as have others, including Mason et al . [4, p. 179], that the reason Liouville’s result works is because the numbers generated are element-by-element… CONTINUE READING
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