On the average of the sum-of-p-prime-divisors function
S. D. Adhikari, G. Coppola, Anirban Mukhopadhyay (2002)
Acta Arithmetica
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S. D. Adhikari, G. Coppola, Anirban Mukhopadhyay (2002)
Acta Arithmetica
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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.
Shanta Laishram, T. N. Shorey (2004)
Acta Arithmetica
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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.
Y.-F. S. Pétermann (2004)
Acta Arithmetica
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Y.-F. S. Pétermann (2007)
Colloquium Mathematicae
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I give explicit values for the constant implied by an Omega-estimate due to Chen and Chen [CC] on the average of the sum of the divisors of n which are relatively coprime to any given integer a.
Douglas E. Iannucci, Florian Luca (2007)
Acta Arithmetica
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Filip, Ferdinánd, Liptai, Kálmán, Tóth, János (2006)
Annales Mathematicae et Informaticae
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Paul Erdős, Péter Kiss, Carl Pomerance (1991)
Acta Arithmetica
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Chen, Yong-Gao, Fang, Jin-Hui (2008)
Integers
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J. Turk (1980)
Journal für die reine und angewandte Mathematik
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R. Mollin, H. Williams (1990)
Acta Arithmetica
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Kevin Broughan, Kevin Ford, Florian Luca (2013)
Colloquium Mathematicae
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If n is a positive integer such that ϕ(n)σ(n) = m² for some positive integer m, then m ≤ n. We put m = n-a and we study the positive integers a arising in this way.
P. Erdös, R. Hall (1974)
Acta Arithmetica
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Clifford Queen (1974)
Acta Arithmetica
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Robert Robson (1985/86)
Mathematische Annalen
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I. R. Shafarevich (1998)
The Teaching of Mathematics
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Davis, Simon (2003)
International Journal of Mathematics and Mathematical Sciences
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