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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
Sequence in context: A077006 A166981 A004394 * A355304 A137425 A141320
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 March 18 21:02 EDT 2024. Contains 370951 sequences. (Running on oeis4.)