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Volume 9, Issue 1 (2021), Pages [1] - [85]
ON THE RATIO OF THE ARITHMETIC AND GEOMETRIC MEANS OF THE FIRST n TERMS OF SOME GENERAL SEQUENCES
[1] C. Axler, On the arithmetic and geometric means of the first n prime numbers, Mediterranean Journal of Mathematics 15(3) (2018); Article 93.
DOI: https://doi.org/10.1007/s00009-018-1137-5
[2] M. Cipolla, La determinazione assintotica dell’ 
numero primo, Rendiconto dell’Accademia delle Scienze Fisiche e Matematiche: Serie 3 8 (1902), 132-166.
[3] M. Hassani, On the ratio of the arithmetic and geometric means of the prime numbers and the number e, International Journal of Number Theory 9(6) (2013), 1593-1603.
DOI: https://doi.org/10.1142/S1793042113500450
[4] R. Jakimczuk, Functions of slow increase and integer sequences, Journal of Integer Sequences 13(1) (2010); Article 10.1.1.
[5] R. Jakimczuk, Integer sequences, functions of slow increase, and the
[6] R. Jakimczuk, Sums of primes: An asymptotic expansion, International Journal of Contemporary Mathematical Sciences 9(16) (2014), 761-765.
DOI: https://doi.org/10.12988/ijcms.2014.411115
[7] R. Jakimczuk, Generalization of some sums on primes and asymptotic expansions, Transnational Journal of Mathematical Analysis and Applications 9(1) (2021), 23-32.
[8] R. Jakimczuk, A simple proof that the square-free numbers have density 
Gulf Journal of Mathematics 1(2) (2013), 85-88.
[9] R. Jakimczuk, The kernel of powerful numbers, International Mathematical Forum 12(15) (2017), 721-730.
DOI: https://doi.org/10.12988/imf.2017.7759
[10] R. Jakimczuk, On the distribution of perfect powers, Journal of Integer Sequences 14(8) (2011); Article 11.8.5.
[11] R. P. Kubelka, Means to an end, Mathematics Magazine 74(2) (2001), 141-142.
DOI: https://doi.org/10.1080/0025570X.2001.11953052
[12] L. Panaitopol, A formula for .gif){kind=small}
applied to a result of Koninck-Ivić, Niew Archief Voor Wiskunde 5/1 (2000), 55-56.
[13] J. Rey Pastor, P. Pi Calleja and C. Trejo, Análisis Matemático, Volume 1, Kapelusz, 1969.
[14] J. B. Rosser and L. Schoenfeld, Approximate formulas for some functions of prime numbers, Illinois Journal of Mathematics 6(1) (1962), 64-94.