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On the mean value of the function \( {\bar{S}_k}(n) \)

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An asymptotic formula is constructed for the mean value of the function \( {\bar{S}_k}(n) \) dual to the Smarandache function S k (n). The O- and Ω-estimates for the second moment of the remainder are obtained.

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Author information

Correspondence to P.D. Varbanets.

Additional information

Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 63, No. 4, pp. 448–458, April, 2011

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Varbanets, P., Kirbat, S.A. On the mean value of the function \( {\bar{S}_k}(n) \) . Ukr Math J 63, 516 (2011). https://doi.org/10.1007/s11253-011-0520-1

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Keywords

  • Asymptotic Formula
  • Dirichlet Series
  • Schwarz Inequality
  • Riemann Zeta Function
  • Euler Gamma Function