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Displaying similar documents to “On fluctuations in the mean of a sum-of-divisors function”

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.

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.

On fluctuations in the mean of a sum-of-divisors function, II

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.

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.

On a divisibility problem

Horst Alzer, József Sándor (2013)

Rendiconti del Seminario Matematico della Università di Padova

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On ramifications divisors of functions in a punctured compact Riemann surface.

Pascual Cutillas Ripoll (1989)

Publicacions Matemàtiques

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Let ν be a compact Riemann surface and ν' be the complement in ν of a nonvoid finite subset. Let M(ν') be the field of meromorphic functions in ν'. In this paper we study the ramification divisors of the functions in M(ν') which have exponential singularities of finite degree at the points of ν-ν', and one proves, for instance, that if a function in M(ν') belongs to the subfield generated by the functions of this type, and has a finite ramification divisor, it also has a finite divisor....