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Let An be a strictly increasing sequence of positive integers such that An ∼ nsf(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).
- Functions of slow increase
- Integer sequences
- The e number
- Numbers with a fixed number of primes in their prime factorization
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Cite this paperAPA
Jakimczuk, R. (2017). On Limits and Formulae where Functions of Slow Increase Appear. Notes on Number Theory and Discrete Mathematics, 23(4), 42-51.Chicago
Jakimczuk, Rafael. “On Limits and Formulae where Functions of Slow Increase Appear.” Notes on Number Theory and Discrete Mathematics 23, no. 4 (2017): 42-51.MLA
Jakimczuk, Rafael. “On limits and formulae where functions of slow increase appear.” Notes on Number Theory and Discrete Mathematics 23.4 (2017): 42-51. Print.