login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A058210 Floor( exp(gamma) n log log n ), where gamma is Euler's constant (A001620). 5
-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 (list; graph; refs; listen; history; text; internal format)
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.

MATHEMATICA

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

CROSSREFS

See A058209.

Sequence in context: A194739 A194765 A239229 * A274414 A079550 A226430

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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 26 14:48 EDT 2019. Contains 321497 sequences. (Running on oeis4.)