On Common and "Perfect" Magic Squares
F. Latoon
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F. Latoon
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Akira Takaku (1987)
Colloquium Mathematicae
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Min Tang, Xiaoyan Ma, Min Feng (2016)
Colloquium Mathematicae
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For a positive integer n, let σ(n) denote the sum of the positive divisors of n. We call n a near-perfect number if σ(n) = 2n + d where d is a proper divisor of n. We show that the only odd near-perfect number with four distinct prime divisors is 3⁴·7²·11²·19².
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.
Asadulla, Syed (1986)
International Journal of Mathematics and Mathematical Sciences
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McDaniel, Wayne L. (1990)
International Journal of Mathematics and Mathematical Sciences
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Sándor, József (2004)
JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]
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Gimbel, Steven, Jaroma, John H. (2003)
Integers
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Deshpande, M.N. (1998)
Portugaliae Mathematica
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Roger Clement Crocker (2008)
Colloquium Mathematicae
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It can be shown that the positive integers representable as the sum of two squares and one power of k (k any fixed integer ≥ 2) have positive density, from which it follows that those integers representable as the sum of two squares and (at most) two powers of k also have positive density. The purpose of this paper is to show that there is an infinity of positive integers not representable as the sum of two squares and two (or fewer) powers of k, k again any fixed integer ≥ 2. ...
Heping Zhang, Xiangqian Zhou (2016)
Discussiones Mathematicae Graph Theory
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A polyomino graph P is a connected finite subgraph of the infinite plane grid such that each finite face is surrounded by a regular square of side length one and each edge belongs to at least one square. A dimer covering of P corresponds to a perfect matching. Different dimer coverings can interact via an alternating cycle (or square) with respect to them. A set of disjoint squares of P is a resonant set if P has a perfect matching M so that each one of those squares is M-alternating....
Nielsen, Pace P. (2003)
Integers
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Paul Rowe (2005)
Acta Arithmetica
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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.
Sándor, József, Kovács, Lehel István (2009)
Acta Universitatis Sapientiae. Mathematica
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Cohen, Graeme L., te Riele, Herman J.J. (1996)
Experimental Mathematics
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De Koninck, Jean-Marie, Ivić, Aleksandar (1998)
Publications de l'Institut Mathématique. Nouvelle Série
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