A058210 a(n) = floor( exp(gamma) n log log n ), where gamma is Euler's constant (A001620).

-2, 0, 2, 4, 6, 8, 10, 12, 14, 17, 19, 21, 24, 26, 29, 31, 34, 36, 39, 41, 44, 46, 49, 52, 54, 57, 60, 62, 65, 68, 70, 73, 76, 79, 81, 84, 87, 90, 92, 95, 98, 101, 104, 107, 109, 112, 115, 118, 121, 124, 127, 130, 133, 135, 138, 141, 144, 147, 150

Offset: 2

Author

N. J. A. Sloane, Nov 30 2000

Keywords

• sign

Comments

Theorem (G. Robin): exp(gamma) n log log n > sigma(n) for all n >= 5041 if and only if the Riemann Hypothesis is true.

Note that a(n) <= exp(gamma) n log log n < a(n) + 1.

References

• D. S. Mitrinovic et al., Handbook of Number Theory, Kluwer, Section III.2.2.b.
• G. Robin, Grandes valeurs de la fonction somme des diviseurs et hypothese de Riemann, J. Math. Pures Appl. 63 (1984), 187-213.

Links

• G. C. Greubel, Table of n, a(n) for n = 2..1000
• 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.
• G. Caveney, J.-L. Nicolas and J. Sondow, On SA, CA, and GA numbers, Ramanujan J., 29 (2012), 359-384.

Crossrefs

See A058209.

Cf. A001620.

Programs

Maple

a:= n-> floor(exp(gamma)*n*log(log(n))):
seq(a(n), n=2..60);  # Alois P. Heinz, Oct 18 2022

Mathematica

Table[Floor[Exp[EulerGamma]*n*Log[Log[n]]], {n,2,50}] (* G. C. Greubel, Dec 31 2016 *)

Extensions

Statement of Robin's theorem corrected by Jonathan Sondow, May 30 2011