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A306633
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Decimal expansion of zeta(2)/zeta(3).
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22
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1, 3, 6, 8, 4, 3, 2, 7, 7, 7, 6, 2, 0, 2, 0, 5, 8, 7, 5, 7, 3, 6, 7, 6, 5, 8, 5, 3, 9, 8, 4, 7, 9, 1, 9, 4, 1, 1, 3, 0, 8, 1, 3, 9, 1, 4, 6, 5, 2, 4, 1, 3, 9, 2, 2, 0, 7, 7, 3, 5, 3, 1, 9, 2, 7, 6, 8, 3, 4, 4, 9, 7, 9, 7, 8, 7, 6, 0, 1, 9, 4, 2, 2, 8, 2, 2, 0
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OFFSET
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1,2
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COMMENTS
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Equals the asymptotic mean of the unitary abundancy index, lim_{n->oo} (1/n) * Sum{k=1..n} usigma(k)/k, where usigma(k) is the sum of the unitary divisors of k (A034448).
Equals the asymptotic mean of the abundancy index of the squarefree numbers (A005117).
In general, the asymptotic mean of the abundancy index of the k-free numbers (numbers that are not divisible by a k-th power other than 1) is zeta(2)/zeta(k+1) (Jakimczuk and Lalín, 2022). (End)
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LINKS
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FORMULA
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Equals Sum_{k>=1} phi(k)/k^3, where phi is the Euler totient function (A000010). - Amiram Eldar, Jun 23 2020
Equals Product_{p prime} (1 + 1/(p*(p+1))). - Amiram Eldar, Aug 10 2020
Equals Sum_{k>=1} mu(k)^2/(k*psi(k)) (the sum of reciprocals of the squarefree numbers multiplied by their Dedekind psi function values, A001615). - Amiram Eldar, Aug 18 2020
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EXAMPLE
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1.3684327776202058757367658539847919411308139146524...
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MATHEMATICA
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RealDigits[Zeta[2]/Zeta[3], 10, 100][[1]]
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PROG
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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