Bi-unitary perfect numbers
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- by Charles R. Wall PDF
- Proc. Amer. Math. Soc. 33 (1972), 39-42 Request permission
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
- M. V. Subbarao, Research Problems: Are There an Infinity of Unitary Perfect Numbers?, Amer. Math. Monthly 77 (1970), no. 4, 389–390. MR 1535865, DOI 10.2307/2316150
- M. V. Subbarao and L. J. Warren, Unitary perfect numbers, Canad. Math. Bull. 9 (1966), 147–153. MR 195796, DOI 10.4153/CMB-1966-018-4 C. R. Wall, A new unitary perfect number, Notices Amer. Math. Soc. 16 (1969), 825. Abstract #69T-A139.
- Charles R. Wall, The fifth unitary perfect number, Canad. Math. Bull. 18 (1975), no. 1, 115–122. MR 376515, DOI 10.4153/CMB-1975-021-9
Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 33 (1972), 39-42
- MSC: Primary 10.05
- DOI: https://doi.org/10.1090/S0002-9939-1972-0289403-9
- MathSciNet review: 0289403