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A197639 GA2 numbers: n with G(n) >= G(a*n) for all integers a > 0, where G(k) = sigma(k)/(k*log(log(k))) and sigma(k) = sum of divisors of k.

%I A197639 #21 Jan 30 2019 05:20:06
%S A197639 3,4,5,6,8,10,12,18,24,36,48,60,72,120,180,240,360,2520,5040
%N A197639 GA2 numbers: n with G(n) >= G(a*n) for all integers a > 0, where G(k) = sigma(k)/(k*log(log(k))) and sigma(k) = sum of divisors of k.
%C A197639 Subsequence of A067698.
%C A197639 A member > 5040 exists iff the Riemann Hypothesis is false, in which case the sequence is infinite. In any case, 3 and 5 are the only odd members. (See Sections 1 and 4 of "On SA, CA, and GA numbers".)
%H A197639 G. Caveney, J.-L. Nicolas, and J. Sondow, <a href="http://math.colgate.edu/~integers/l33/l33.Abstract.html">Robin's theorem, primes, and a new elementary reformulation of the Riemann Hypothesis</a>, Integers 11 (2011), article A33.
%H A197639 G. Caveney, J.-L. Nicolas and J. Sondow, <a href="http://arxiv.org/abs/1112.6010">On SA, CA, and GA numbers</a>, arXiv:1112.6010 [math.NT], 2011-2012; Ramanujan J., 29 (2012), 359-384.
%t A197639 nmax = 10^6; amax = 10;
%t A197639 G[k_] := DivisorSigma[1, k]/(k Log[Log[k]]);
%t A197639 okQ[n_] := DivisorSigma[1, n] > n Exp[EulerGamma] Log[Log[n]] && AllTrue[ Range[amax], Function[a, G[n] >= G[a*n]]];
%t A197639 Reap[For[n = 1, n <= nmax, n++, If[okQ[n], Print[n]; Sow[n]]]][[2, 1]] (* _Jean-François Alcover_, Jan 30 2019 *)
%Y A197639 Cf. A000203, A067698, A197638, A201557.
%K A197639 nonn
%O A197639 1,1
%A A197639 Geoffrey Caveney, Jean-Louis Nicolas, and _Jonathan Sondow_, Dec 02 2011