On a diophantine equation of a modified Fermat type
Kustaa Inkeri (1989)
Acta Arithmetica
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Kustaa Inkeri (1989)
Acta Arithmetica
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Filip, Ferdinánd, Liptai, Kálmán, Tóth, János (2006)
Annales Mathematicae et Informaticae
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Shi-Chao Chen, Yong-Gao Chen (2004)
Colloquium Mathematicae
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We prove an Ω result on the average of the sum of the divisors of n which are relatively coprime to any given integer a. This generalizes the earlier result for a prime proved by Adhikari, Coppola and Mukhopadhyay.
Titu Andreescu, Florian Luca, M. Tip Phaovibul (2016)
Acta Arithmetica
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We prove that there are no strings of three consecutive integers each divisible by the number of its divisors, and we give an estimate for the number of positive integers n ≤ x such that each of n and n + 1 is a multiple of the number of its divisors.
S. D. Adhikari, G. Coppola, Anirban Mukhopadhyay (2002)
Acta Arithmetica
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Shanta Laishram, T. N. Shorey (2004)
Acta Arithmetica
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I. R. Shafarevich (1998)
The Teaching of Mathematics
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Wacław Sierpiński
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Clifford Queen (1974)
Acta Arithmetica
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Chen, Yong-Gao, Fang, Jin-Hui (2008)
Integers
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Florian Luca, Carl Pomerance (2015)
Acta Arithmetica
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Answering a question of Erdős, we show that a positive proportion of even numbers are in the form s(n), where s(n) = σ(n) - n, the sum of proper divisors of n.
Győry, Kálmán, Smyth, Chris (2010)
Integers
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Davis, Simon (2003)
International Journal of Mathematics and Mathematical Sciences
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Mazur, Marcin (2006)
Integers
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