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A058210
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a(n) = floor( exp(gamma) n log log n ), where gamma is Euler's constant (A001620).
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5
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-2, 0, 2, 4, 6, 8, 10, 12, 14, 17, 19, 21, 24, 26, 29, 31, 34, 36, 39, 41, 44, 46, 49, 52, 54, 57, 60, 62, 65, 68, 70, 73, 76, 79, 81, 84, 87, 90, 92, 95, 98, 101, 104, 107, 109, 112, 115, 118, 121, 124, 127, 130, 133, 135, 138, 141, 144, 147, 150
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OFFSET
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2,1
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COMMENTS
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Theorem (G. Robin): exp(gamma) n log log n > sigma(n) for all n >= 5041 if and only if the Riemann Hypothesis is true.
Note that a(n) <= exp(gamma) n log log n < a(n) + 1.
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REFERENCES
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D. S. Mitrinovic et al., Handbook of Number Theory, Kluwer, Section III.2.2.b.
G. Robin, Grandes valeurs de la fonction somme des diviseurs et hypothese de Riemann, J. Math. Pures Appl. 63 (1984), 187-213.
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LINKS
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MAPLE
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a:= n-> floor(exp(gamma)*n*log(log(n))):
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MATHEMATICA
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Table[Floor[Exp[EulerGamma]*n*Log[Log[n]]], {n, 2, 50}] (* G. C. Greubel, Dec 31 2016 *)
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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