Abstract
Let A be a set of positive integers. For a fixed \(k \ge 1\) and a positive integer n let \(R_{A, k}(n)\) denote the number of representations of n as the sum of k terms from the set A. In this paper we give a necessary and sufficient condition to the multiplicativity of the function \(c_{1}R_{A, 1}(n) + c_{2}R_{A, 2}(n)\), where \(c_1\) and \(c_2\) are integers and \(c_{2} \ne 0\).
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Sándor Z. Kiss was supported by the OTKA Grant No. NK105645. This research was partially supported by the National Research, Development and Innovation Office—NKFIH, K115288. Csaba Sándor was supported by the OTKA Grant No. K109789. This paper was supported by the János Bolyai Research Scholarship of the Hungarian Academy of Sciences.
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Kiss, S.Z., Sándor, C. On the multiplicativity of the linear combination of additive representation functions. Ramanujan J 44, 385–399 (2017). https://doi.org/10.1007/s11139-016-9811-3
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DOI: https://doi.org/10.1007/s11139-016-9811-3