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Search: id:A058209
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| A058209 |
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[ exp(gamma) n log log n ] - sigma(n), where gamma is Euler's constant (A001620) and sigma(n) is sum of divisors of n (A000203). |
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+0
6
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| -5, -4, -5, -2, -6, 0, -5, -1, -4, 5, -9, 7, 0, 2, -2, 13, -5, 16, -3, 9, 8, 22, -11, 21, 12, 17, 4, 32, -7, 36, 7, 25, 22, 31, -10, 46, 27, 34, 2, 53, 2, 57, 20, 29, 37, 64, -9, 61, 28, 52, 29, 76, 13, 63, 18, 61, 54, 87, -18, 91, 60, 55, 35, 81, 24, 103, 48, 81, 36, 111, -9, 115
(list; graph; listen)
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OFFSET
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2,1
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COMMENT
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Theorem (G. Robin): sequence is positive for all n >= 5041 if and only if the Riemann Hypothesis is true.
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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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MAPLE
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with(numtheory); Digits := 100; g := evalf(gamma); [seq( floor(exp(g)*n*log(log(n)))-sigma[1](n), n=2..80)];
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CROSSREFS
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Cf. A000203, A001620, A057641, A057642, A058210.
Sequence in context: A019117 A123587 A018840 this_sequence A160789 A131291 A131369
Adjacent sequences: A058206 A058207 A058208 this_sequence A058210 A058211 A058212
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KEYWORD
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sign,nice,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Nov 30 2000
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