Rafael Jakimczuk

Notes on Number Theory and Discrete Mathematics

Print ISSN 1310–5132, Online ISSN 2367–8275

Volume 23, 2017, Number 4, Pages 42—51

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## Details

### Authors and affiliations

Rafael Jakimczuk

*División Matemática, Universidad Nacional de Luján
Buenos Aires, Argentina
*

### Abstract

Let *A _{n}* be a strictly increasing sequence of positive integers such that

*A*∼

_{n}*n*(

^{s}f*n*), where

*f*(

*x*) is a function of slow increase and

*s*is a positive real number. In this article we obtain some limits and asymptotic formulae where appear functions of slow increase. As example, we apply the obtained results to the sequence of numbers with exactly

*k*prime factors in their prime factorization, in particular to the sequence of prime numbers (

*k*= 1).

### Keywords

- Functions of slow increase
- Integer sequences
- The
*e*number - Limits
- Numbers with a fixed number of primes in their prime factorization

### AMS Classification

- 11A99
- 11B99

### References

- Jakimczuk, R. (2007) The ratio between the average factor in a product and the last factor, Mathematical Sciences: Quarterly Journal, 1, 53–62.
- Jakimczuk, R. (2010) Functions of slow increase and integer sequences, Journal of Integer Sequences, 13, Article 10.1.1.
- Jakimczuk, R. (2016) On a limit where appear prime numbers, Notes on Number Theory and Discrete Mathematics, 22(1), 1–4.
- Sándor, J. (2012) On certain bounds and limits for prime numbers, Notes on Number Theory and Discrete Mathematics, 18(1), 1–5.
- Sándor, J. & Verroken A. (2011) On a limit involving the product of prime numbers, Notes on Number Theory and Discrete Mathematics, 17(2), 1–3.

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## Cite this paper

Jakimczuk, R. (2017). On Limits and Formulae where Functions of Slow Increase Appear. Notes on Number Theory and Discrete Mathematics, 23(4), 42-51.