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→The density of the k-th power free integers in {{math|N}}: add a missing ) |
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The function ''δ'' is multiplicative, and since it is bounded by 1, its [[Dirichlet series]] converges absolutely in the half-plane Re(s)>1, and there has [[Euler product]]
<math>\sum_{Q_k}n^{-s}=\sum_{n}\delta(n)n^{-s}=\prod_{p}(1+p^{-s}+\cdots +p^{-s(k-1)})=\prod_{p}\left(\frac{1-p^{-sk}}{1-p^{-s}}\right)=\frac{\zeta(s)}{\zeta(sk)}</math>.
By the [[Möbius inversion]] formula, we get
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