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A308043
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Decimal expansion of the asymptotic mean of 2^omega(k)/d(k), where omega(k) is the number of distinct prime divisors of k (A001221) and d(k) is its number of divisors (A000005).
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7
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8, 1, 9, 1, 9, 0, 9, 6, 4, 1, 4, 8, 9, 9, 1, 9, 0, 8, 1, 8, 0, 3, 6, 5, 6, 6, 0, 3, 8, 1, 3, 7, 3, 5, 8, 2, 7, 2, 2, 2, 6, 8, 8, 5, 2, 4, 7, 9, 7, 1, 8, 4, 9, 8, 5, 8, 2, 1, 4, 6, 6, 0, 3, 7, 6, 2, 1, 1, 7, 4, 3, 5, 0, 4, 7, 2, 2, 0, 4, 0, 2, 2, 0, 8, 7, 0, 7
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OFFSET
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0,1
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COMMENTS
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Also the asymptotic mean of the ratio between the number of unitary divisors and the number of divisors of the integers.
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LINKS
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FORMULA
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Equals Product_{p prime} (1-1/p)*(2*p*log(p/(p-1))-1).
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EXAMPLE
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0.81919096414899190818036566038137358272226885247971...
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MATHEMATICA
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$MaxExtraPrecision = 1000; m = 1000; f[p_] := (1 - 1/p)*(2*p*Log[p/(p - 1)] - 1); c = Rest[CoefficientList[Series[Log[f[1/x]], {x, 0, m}], x]]; RealDigits[f[2] * Exp[ NSum[ Indexed[c, n]*(PrimeZetaP[n] - 1/2^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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