• Title/Summary/Keyword: $M{\ddot{o}}bius$ inversion formula

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GENERALIZATIONS OF NUMBER-THEORETIC SUMS

  • Kanasri, Narakorn Rompurk;Pornsurat, Patchara;Tongron, Yanapat
    • Communications of the Korean Mathematical Society
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    • v.34 no.4
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    • pp.1105-1115
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    • 2019
  • 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.