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Values of n for which sigma(n) < e^gamma * n * log(log(n)).
5

%I #23 Aug 13 2015 21:22:02

%S 7,11,13,14,15,17,19,21,22,23,25,26,27,28,29,31,32,33,34,35,37,38,39,

%T 40,41,42,43,44,45,46,47,49,50,51,52,53,54,55,56,57,58,59,61,62,63,64,

%U 65,66,67,68,69,70,71,73,74,75,76,77,78,79,80,81,82,83,85,86,87,88,89

%N Values of n for which sigma(n) < e^gamma * n * log(log(n)).

%C sigma(n) < e^gamma * n * log(log(n)) is "Robin's inequality" - see A067698. Sequence is cofinite if and only if the Riemann Hypothesis is true.

%H G. Caveney, J.-L. Nicolas, and J. Sondow, <a href="http://www.integers-ejcnt.org/l33/l33.pdf">Robin's theorem, primes, and a new elementary reformulation of the Riemann Hypothesis</a>, Integers 11 (2011), #A33.

%H G. Caveney, J.-L. Nicolas and J. Sondow, <a href="http://arxiv.org/abs/1112.6010">On SA, CA, and GA numbers</a>, Ramanujan J., 29 (2012), 359-384.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/RobinsTheorem.html">Robin's Theorem</a>

%F a(n) = n + 27 for n > 5039, if and only if the Riemann Hypothesis is true. -_Charles R Greathouse IV_, May 31 2011

%t Select[Range[100], DivisorSigma[1, #] < E^EulerGamma*#*Log[Log[#]] &] (* _Jean-François Alcover_, Oct 30 2012 *)

%Y Cf. A067698.

%K nonn,easy

%O 1,1

%A _Eric W. Weisstein_, Feb 09 2004