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

2,1

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.

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 *)

Crossrefs

See A058209.

Cf. A001620.

Sequence in context: A194739 A194765 A239229 * A360860 A274414 A079550

Adjacent sequences: A058207 A058208 A058209 * A058211 A058212 A058213

Keyword

sign

Author

N. J. A. Sloane, Nov 30 2000

Extensions

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

Status

approved