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Proceedings of the American Mathematical Society

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Recurrences for the sum of divisors


Author: John A. Ewell
Journal: Proc. Amer. Math. Soc. 64 (1977), 214-218
MSC: Primary 10A20
MathSciNet review: 0441836
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Abstract: The author presents two recursive determinations of the sum of positive divisors of a given positive integer. Each recurrence is then discussed with regard to economy of computation, and in this light is compared with the well-known recurrence of Niven and Zuckerman. As far as methods of proof are concerned, everything is accomplished within the algebra of formal power series.


References [Enhancements On Off] (What's this?)

  • [1] G. H. Hardy and E. M. Wright, An introduction to the theory of numbers, 4th ed., Clarendon Press, Oxford, 1960.
  • [2] Ivan Niven and Herbert S. Zuckerman, An introduction to the theory of numbers, 3rd ed., John Wiley & Sons, Inc., New York-London-Sydney, 1972. MR 0344181

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1977-0441836-8
Keywords: Recurrences, sum of the positive divisors of a positive integer, identities
Article copyright: © Copyright 1977 American Mathematical Society