Abstract
For given integersr andk, 0<r<k, any integern>1 is uniquely representable in the formn=d k·m withm k-free (that means there is nok-th prime powerp k dividingm);n is called a (k, r)-integer, ifm isr-free. In the present paper asymptotic formulae are derived for the number of (k, r)-integersn≤x contained in a given arithmetic progression and for the number of representations of a positive integer, as the sum of a (k 1,r 1)-integer and a (k 2,r 2)-integer.
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Literatur
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Brinitzer, E. Über (k, r)-Zahlen. Monatshefte für Mathematik 80, 31–35 (1975). https://doi.org/10.1007/BF01487801
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DOI: https://doi.org/10.1007/BF01487801