cp's OEIS Frontend

A058210 a(n) = floor( exp(gamma) n log log n ), where gamma is Euler's constant (A001620).

%I A058210 #20 Oct 18 2022 17:58:31
%S A058210 -2,0,2,4,6,8,10,12,14,17,19,21,24,26,29,31,34,36,39,41,44,46,49,52,
%T A058210 54,57,60,62,65,68,70,73,76,79,81,84,87,90,92,95,98,101,104,107,109,
%U A058210 112,115,118,121,124,127,130,133,135,138,141,144,147,150
%N A058210 a(n) = floor( exp(gamma) n log log n ), where gamma is Euler's constant (A001620).
%C A058210 Theorem (G. Robin): exp(gamma) n log log n > sigma(n) for all n >= 5041 if and only if the Riemann Hypothesis is true.
%C A058210 Note that a(n) <= exp(gamma) n log log n < a(n) + 1.
%D A058210 D. S. Mitrinovic et al., Handbook of Number Theory, Kluwer, Section III.2.2.b.
%D A058210 G. Robin, Grandes valeurs de la fonction somme des diviseurs et hypothese de Riemann, J. Math. Pures Appl. 63 (1984), 187-213.
%H A058210 G. C. Greubel, <a href="/A058210/b058210.txt">Table of n, a(n) for n = 2..1000</a>
%H A058210 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 A058210 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.
%p A058210 a:= n-> floor(exp(gamma)*n*log(log(n))):
%p A058210 seq(a(n), n=2..60);  # _Alois P. Heinz_, Oct 18 2022
%t A058210 Table[Floor[Exp[EulerGamma]*n*Log[Log[n]]], {n,2,50}] (* _G. C. Greubel_, Dec 31 2016 *)
%Y A058210 See A058209.
%Y A058210 Cf. A001620.
%K A058210 sign
%O A058210 2,1
%A A058210 _N. J. A. Sloane_, Nov 30 2000
%E A058210 Statement of Robin's theorem corrected by _Jonathan Sondow_, May 30 2011