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 A189686 Superabundant numbers (A004394) satisfying the reverse of Robin's inequality (A091901). 4
 2, 4, 6, 12, 24, 36, 48, 60, 120, 180, 240, 360, 720, 840, 2520, 5040 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 5040 is the last element in the sequence if and only if the Riemann Hypothesis is true. (See Akbary and Friggstad in A004394.) LINKS G. Caveney, J.-L. Nicolas, and J. Sondow, Robin's theorem, primes, and a new elementary reformulation of the Riemann Hypothesis, Integers 11 (2011), #A33 (see Table 1). G. Caveney, J.-L. Nicolas and J. Sondow, On SA, CA, and GA numbers, arXiv:1112.6010 [math.NT], 2011-2012; Ramanujan J., 29 (2012), 359-384. FORMULA Equals A004394 intersect A067698. MATHEMATICA kmax = 10^4; 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]]]; A067698 = Select[Range[2, kmax], DivisorSigma[1, #] > Exp[EulerGamma] # Log[Log[#]]&]; Intersection[A004394, A067698] (* Jean-François Alcover, Jan 28 2019 *) PROG (PARI) is(n)=sigma(n) >= exp(Euler) * n * log(log(n)); \\ A067698 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 CROSSREFS Cf. A004394, A091901, A067698, A166981, A077006. Sequence in context: A077006 A166981 A004394 * A137425 A141320 A307122 Adjacent sequences:  A189683 A189684 A189685 * A189687 A189688 A189689 KEYWORD nonn AUTHOR Geoffrey Caveney, Jean-Louis Nicolas, and Jonathan Sondow, May 30 2011 EXTENSIONS Erroneous terms 1260 and 1680 removed by Jean-François Alcover, Jan 28 2019 STATUS approved

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Last modified October 17 21:57 EDT 2019. Contains 328134 sequences. (Running on oeis4.)