The Dedekind -function is defined by the divisor product
(1)
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where the product is over the distinct prime factors of , with the special case . The first few values are
(2)
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(3)
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(4)
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(5)
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(6)
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(7)
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(8)
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(9)
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(10)
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(11)
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giving 1, 3, 4, 6, 6, 12, 8, 12, 12, 18, ... (OEIS A001615).
Sums for include
(12)
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(13)
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where is the Möbius function.
The Dirichlet generating function is given by
(14)
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(15)
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where is the Riemann zeta function.