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

2, 4, 6, 12, 24, 36, 48, 60, 120, 180, 240, 360, 720, 840, 2520, 5040

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

Table of n, a(n) for n=1..16.

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 * A355304 A137425 A141320

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