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A308042
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Decimal expansion of the asymptotic mean of d_3(k)/ud_3(k), where d_3(k) is the number of ordered factorizations of k as product of 3 divisors (A007425) and ud_3(k) = 3^omega(k) is the unitary analog of d_3 (A074816).
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3
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2, 2, 2, 4, 1, 6, 2, 4, 8, 3, 8, 0, 1, 8, 6, 9, 5, 8, 4, 4, 2, 1, 7, 4, 8, 8, 9, 4, 5, 4, 6, 9, 0, 0, 3, 7, 8, 5, 7, 6, 0, 0, 0, 8, 0, 8, 5, 1, 4, 2, 8, 7, 6, 4, 3, 8, 0, 4, 3, 3, 6, 2, 7, 5, 2, 8, 7, 9, 0, 8, 6, 0, 5, 3, 8, 4, 4, 8, 9, 9, 3, 9, 9, 3, 3, 5, 7
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OFFSET
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1,1
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LINKS
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FORMULA
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Equals Product_{p prime} (1 - 1/p) * (2 + (1 - 1/p)^(-3)))/3.
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EXAMPLE
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2.22416248380186958442174889454690037857600080851428...
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MATHEMATICA
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$MaxExtraPrecision = 1000; m = 1000; c = LinearRecurrence[{6, -16, 64/3, -32/3}, {0, 8, 32, 224/3}, m]; RealDigits[Exp[NSum[Indexed[c, n]*PrimeZetaP[n]/n/2^n, {n, 2, m}, NSumTerms -> m, WorkingPrecision -> m]], 10, 100][[1]]
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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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