Thirty-nine perfect numbers and their divisors.
Asadulla, Syed (1986)
International Journal of Mathematics and Mathematical Sciences
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Asadulla, Syed (1986)
International Journal of Mathematics and Mathematical Sciences
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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.
McDaniel, Wayne L. (1990)
International Journal of Mathematics and Mathematical Sciences
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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.
P. John, H. Sachs, H. Zernitz (1987)
Applicationes Mathematicae
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Gimbel, Steven, Jaroma, John H. (2003)
Integers
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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 (2004)
JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]
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Tošić, Ratko, Vojvodić, Dušan (2000)
Novi Sad Journal of Mathematics
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M. N. Mukherjee, S. Raychaudhuri (1993)
Matematički Vesnik
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G. L. Garg, B. Kumar (1989)
Matematički Vesnik
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Isaiah Maximoff (1947)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Cohen, Graeme L., te Riele, Herman J.J. (1996)
Experimental Mathematics
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