The Ramanujan Journal

, Volume 35, Issue 1, pp 149–156 | Cite as

Averages of Ramanujan sums: note on two papers by E. Alkan

  • László Tóth


We give a simple proof and a multivariable generalization of an identity due to E. Alkan concerning a weighted average of the Ramanujan sums. We deduce identities for other weighted averages of the Ramanujan sums with weights concerning logarithms, values of arithmetic functions for gcd’s, the Gamma function, the Bernoulli polynomials, and binomial coefficients.


Ramanujan’s sum Jordan’s function Bernoulli numbers and polynomials Gamma function 

Mathematics Subject Classification

11A25 11B68 33B15 


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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Institute of MathematicsUniversität für BodenkulturViennaAustria
  2. 2.Department of MathematicsUniversity of PécsPecsHungary

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