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Bi-unitary perfect numbers

Author: Charles R. Wall
Journal: Proc. Amer. Math. Soc. 33 (1972), 39-42
MSC: Primary 10.05
MathSciNet review: 0289403
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Abstract: Let d be a divisor of a positive integer n. Then d is a unitary divisor if d and n/d are relatively prime, and d is a bi-unitary divisor if the greatest common unitary divisor of d and n/d is 1. An integer is bi-unitaty perfect if it equals the sum of its proper bi-unitary divisors. The purpose of this paper is to show that there are only three bi-unitary perfect numbers, namely 6, 60 and 90.

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

  • [1] M. V. Subbarao, Are there an infinity of unitary perfect numbers?, Amer. Math. Monthly 77 (1970), 389-390. MR 1535865
  • [2] M. V. Subbarao and L. J. Warren, Unitary perfect numbers, Canad. Math. Bull. 9 (1966), 147-153. MR 33 #3994. MR 0195796 (33:3994)
  • [3] C. R. Wall, A new unitary perfect number, Notices Amer. Math. Soc. 16 (1969), 825. Abstract #69T-A139.
  • [4] -, The fifth unitary perfect number, Canad. Math. Bull. (to appear). MR 0376515 (51:12690)

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Keywords: Bi-unitary divisors, perfect numbers
Article copyright: © Copyright 1972 American Mathematical Society

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