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Volume 9, Issue 1 (2021), Pages [1] - [85]

GENERALIZATION OF SOME SUMS ON PRIMES AND ASYMPTOTIC EXPANSIONS 

[1] M. Cipolla, La determinazione assintotica  numero primo, Rend. Acad. Sci. Fis. Mat. Napoli, Ser. 3 8 (1902), 132-166.

 

[2] R. Jakimczuk, An observation on the Cipolla’s expansion, Mathematical Sciences 2(2) (2008), 219-222.

 

[3] R. Jakimczuk, A note on sums of greatest (least) prime factors, International Journal of Contemporary Mathematical Sciences 8(9) (2013), 423-432.

 

DOI: http://dx.doi.org/10.12988/ijcms.2013.13042

 

[4] R. Jakimczuk, Sums of primes: An asymptotic expansion, International Journal of Contemporary Mathematical Sciences 9(16) (2014), 761-765.

 

DOI: http://dx.doi.org/10.12988/ijcms.2014.411115

 

[5] W. J. LeVeque, Topics in Number Theory, Volume II, Addison-Wesley, 1958.

 

[6] J. B. Rosser and L. Schoenfeld, Approximate formulas for some functions of prime numbers, Illinois Journal of Mathematics 6(1) (1962), 64-94.

 

DOI: http://doi.org/10.1215/ijm/1255631807