Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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GENERALIZATIONS OF NUMBER-THEORETIC SUMS

  • Received : 2018.10.02
  • Accepted : 2019.03.15
  • Published : 2019.10.31
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Abstract

For positive integers n and k, let $S_k(n)$ and $S^{\prime}_k(n)$ be the sums of the elements in the finite sets {$x^k:1{\leq}x{\leq}n$, (x, n) = 1} and {$x^k:1{\leq}x{\leq}n/2$, (x, n) = 1}respectively. The formulae for both $S_k(n)$ and $S^{\prime}_k(n)$ are established. The explicit formulae when k = 1, 2, 3 are also given.

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References

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