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REMARKS ON THE ARITHMETICAL FUNCTION $a_{p}(n)$

Year 2020, , 131 - 136, 31.07.2020
https://doi.org/10.33773/jum.637104

Abstract

In this paper,for any arbitrary  two prime numbers $p$ and $q$ the relationship between the corresponding  arithmetic functions  $(a_p(n))$ and  $(a_q(n))$ are investigated.~Furthermore,  the  general formula for  statistical density of all sets on which the two arithmetic functions have the same value  also established.

References

  • \bibitem{1} Fast, H. , (1951) Sur la convergence statistique., \textit{Colloq.Math}, VOL, 2, 241--244.
  • \bibitem{2} Schoenberg, I. J., (1959) The integrability of certain functions and related summability methods, matrix characterization of statistical convergence, \textit{Amer.Math.}, VOL, 66, 361--375.
  • \bibitem{3} Zygmund, A. (1979) \textit{Trigonometric series}, 2nd., Ed. Vol. II, Cambridge Univ. press, London and New York.
  • \bibitem{4} {\v{S}}al{\'a}t, T., (1994) On the function $ a_{p},~p^{a_{p}(n)} \backslash\backslash ~ n ~(n>1)$ , \textit{Mathematica Slovaca}, VOL, 44, Num, 2 143--151.
  • \bibitem{5} Feh{\'e}ra, Zolt{\'a}n and L{\'a}szl{\'o}a, B{\'e}la and Ma{\v{c}}ajb, Martin and {\v{S}}al{\'a}tb, Tibor, 2006,Remarks on arithmetical functions $ap (n)$, $\gamma$ (n), $\tau$ (n),Annales Mathematicae et Informaticae,Vol 33,35-43
  • \bibitem{6} Abdu Awel and M. K\"{u}\c{c}\"{u}kaslan ,A Note On Limit And Cluster Points Of The Arithmetical Functions,J.Indones.Math.Soc(under review)
  • \bibitem{10} Milan, P. (2017) \textit{DENSITY AND RELATED TOPICS}, Mathematics Institute slovak Acadamic of Sciences
Year 2020, , 131 - 136, 31.07.2020
https://doi.org/10.33773/jum.637104

Abstract

References

  • \bibitem{1} Fast, H. , (1951) Sur la convergence statistique., \textit{Colloq.Math}, VOL, 2, 241--244.
  • \bibitem{2} Schoenberg, I. J., (1959) The integrability of certain functions and related summability methods, matrix characterization of statistical convergence, \textit{Amer.Math.}, VOL, 66, 361--375.
  • \bibitem{3} Zygmund, A. (1979) \textit{Trigonometric series}, 2nd., Ed. Vol. II, Cambridge Univ. press, London and New York.
  • \bibitem{4} {\v{S}}al{\'a}t, T., (1994) On the function $ a_{p},~p^{a_{p}(n)} \backslash\backslash ~ n ~(n>1)$ , \textit{Mathematica Slovaca}, VOL, 44, Num, 2 143--151.
  • \bibitem{5} Feh{\'e}ra, Zolt{\'a}n and L{\'a}szl{\'o}a, B{\'e}la and Ma{\v{c}}ajb, Martin and {\v{S}}al{\'a}tb, Tibor, 2006,Remarks on arithmetical functions $ap (n)$, $\gamma$ (n), $\tau$ (n),Annales Mathematicae et Informaticae,Vol 33,35-43
  • \bibitem{6} Abdu Awel and M. K\"{u}\c{c}\"{u}kaslan ,A Note On Limit And Cluster Points Of The Arithmetical Functions,J.Indones.Math.Soc(under review)
  • \bibitem{10} Milan, P. (2017) \textit{DENSITY AND RELATED TOPICS}, Mathematics Institute slovak Acadamic of Sciences
There are 7 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Abdu Awel Adem 0000-0002-0279-3564

Publication Date July 31, 2020
Submission Date October 23, 2019
Acceptance Date February 13, 2021
Published in Issue Year 2020

Cite

APA Adem, A. A. (2020). REMARKS ON THE ARITHMETICAL FUNCTION $a_{p}(n)$. Journal of Universal Mathematics, 3(2), 131-136. https://doi.org/10.33773/jum.637104
AMA Adem AA. REMARKS ON THE ARITHMETICAL FUNCTION $a_{p}(n)$. JUM. July 2020;3(2):131-136. doi:10.33773/jum.637104
Chicago Adem, Abdu Awel. “REMARKS ON THE ARITHMETICAL FUNCTION $a_{p}(n)$”. Journal of Universal Mathematics 3, no. 2 (July 2020): 131-36. https://doi.org/10.33773/jum.637104.
EndNote Adem AA (July 1, 2020) REMARKS ON THE ARITHMETICAL FUNCTION $a_{p}(n)$. Journal of Universal Mathematics 3 2 131–136.
IEEE A. A. Adem, “REMARKS ON THE ARITHMETICAL FUNCTION $a_{p}(n)$”, JUM, vol. 3, no. 2, pp. 131–136, 2020, doi: 10.33773/jum.637104.
ISNAD Adem, Abdu Awel. “REMARKS ON THE ARITHMETICAL FUNCTION $a_{p}(n)$”. Journal of Universal Mathematics 3/2 (July 2020), 131-136. https://doi.org/10.33773/jum.637104.
JAMA Adem AA. REMARKS ON THE ARITHMETICAL FUNCTION $a_{p}(n)$. JUM. 2020;3:131–136.
MLA Adem, Abdu Awel. “REMARKS ON THE ARITHMETICAL FUNCTION $a_{p}(n)$”. Journal of Universal Mathematics, vol. 3, no. 2, 2020, pp. 131-6, doi:10.33773/jum.637104.
Vancouver Adem AA. REMARKS ON THE ARITHMETICAL FUNCTION $a_{p}(n)$. JUM. 2020;3(2):131-6.