On the limiting distribution of a generalized divisor problem for the case -1/2 < a < 0
Yuk-Kam Lau (2001)
Acta Arithmetica
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Displaying similar documents to “Some distribution problems concerning the divisors of integers”
On the limiting distribution of a generalized divisor problem for the case -1/2 < a < 0
On consecutive integers divisible by the number of their divisors
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.
The Distribution of Integers n Divisible by Lomega(n)
F. Luca, A. Sankaranarayanan (2004)
Publications de l'Institut Mathématique
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On the limiting distribution of a generalized divisor problem for the case -1 ≤ a < -1/2
Yuk-Kam Lau (2001)
Acta Arithmetica
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On the distribution of some integers related to perfect and amicable numbers
Paul Pollack, Carl Pomerance (2013)
Colloquium Mathematicae
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On fluctuations in the mean of a sum-of-divisors function
Y.-F. S. Pétermann (2004)
Acta Arithmetica
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The range of the sum-of-proper-divisors function
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.
The jumping champions of the Farey series
Cristian Cobeli, Kevin Ford, Alexandru Zaharescu (2003)
Acta Arithmetica
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On the average of the sum-of-a-divisors function
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.
Triangular numbers whose sum of divisors is also triangular
Douglas E. Iannucci, Florian Luca (2007)
Acta Arithmetica
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Possible relationship existing in the distribution of electrolyte between the soap and the lye.
Eddy, N.O., Ukpong, I.J. (2006)
APPS. Applied Sciences
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On irregularities of distribution, IV
K. Roth (1980)
Acta Arithmetica
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On the robustness of properties characterizing the normal distribution
Boguslawa Bednarek-Kozek, A. Kozek (1972)
Applicationes Mathematicae
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On the composition of the Euler function and the sum of divisors function
Jean-Marie De Koninck, Florian Luca (2007)
Colloquium Mathematicae
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Let H(n) = σ(ϕ(n))/ϕ(σ(n)), where ϕ(n) is Euler's function and σ(n) stands for the sum of the positive divisors of n. We obtain the maximal and minimal orders of H(n) as well as its average order, and we also prove two density theorems. In particular, we answer a question raised by Golomb.