cp's OEIS Frontend

A189686 Superabundant numbers (A004394) satisfying the reverse of Robin's inequality (A091901).

%I A189686 #27 Jan 29 2019 04:36:16
%S A189686 2,4,6,12,24,36,48,60,120,180,240,360,720,840,2520,5040
%N A189686 Superabundant numbers (A004394) satisfying the reverse of Robin's inequality (A091901).
%C A189686 5040 is the last element in the sequence if and only if the Riemann Hypothesis is true. (See Akbary and Friggstad in A004394.)
%H A189686 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), #A33 (see Table 1).
%H A189686 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.
%F A189686 Equals A004394 intersect A067698.
%t A189686 kmax = 10^4;
%t A189686 A004394 = Join[{1}, Reap[For[r = 1; k = 2, k <= kmax, k = k + 2, s = DivisorSigma[-1, k]; If[s > r, r = s; Sow[k]]]][[2, 1]]];
%t A189686 A067698 = Select[Range[2, kmax], DivisorSigma[1, #] > Exp[EulerGamma] # Log[Log[#]]&];
%t A189686 Intersection[A004394, A067698] (* _Jean-François Alcover_, Jan 28 2019 *)
%o A189686 (PARI) is(n)=sigma(n) >= exp(Euler) * n * log(log(n)); \\ A067698
%o A189686 lista(nn) = my(r=1, t); forstep(n=2, nn, 2, t=sigma(n, -1); if(t>r && is(n), r=t; print1(n, ", "))); \\ _Michel Marcus_, Jan 28 2019; adapted from A004394
%Y A189686 Cf. A004394, A091901, A067698, A166981, A077006.
%K A189686 nonn
%O A189686 1,1
%A A189686 Geoffrey Caveney, Jean-Louis Nicolas, and _Jonathan Sondow_, May 30 2011
%E A189686 Erroneous terms 1260 and 1680 removed by _Jean-François Alcover_, Jan 28 2019