A Unified Theory of Perfect and Related Functions
M. N. Mukherjee, S. Raychaudhuri (1993)
Matematički Vesnik
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M. N. Mukherjee, S. Raychaudhuri (1993)
Matematički Vesnik
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P. John, H. Sachs, H. Zernitz (1987)
Applicationes Mathematicae
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G. L. Garg, B. Kumar (1989)
Matematički Vesnik
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A. Błaszczyk (1973)
Colloquium Mathematicae
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Tošić, Ratko, Vojvodić, Dušan (2000)
Novi Sad Journal of Mathematics
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Min Tang, Xiao-Zhi Ren, Meng Li (2013)
Colloquium Mathematicae
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For a positive integer n, let σ(n) denote the sum of the positive divisors of n. Let d be a proper divisor of n. We call n a near-perfect number if σ(n) = 2n + d, and a deficient-perfect number if σ(n) = 2n - d. We show that there is no odd near-perfect number with three distinct prime divisors and determine all deficient-perfect numbers with at most two distinct prime factors.
Ivan Gutman (1991)
Publications de l'Institut Mathématique
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David Holgate (1998)
Commentationes Mathematicae Universitatis Carolinae
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We define perfect morphisms to be those which are the pullback of their image under a given endofunctor. The interplay of these morphisms with other generalisations of perfect maps is investigated. In particular, closure operator theory is used to link closure and orthogonality properties of such morphisms. A number of detailed examples are given.
Tomohiro Yamada (2005)
Colloquium Mathematicae
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We show that there is an effectively computable upper bound of odd perfect numbers whose Euler factors are powers of fixed exponent.