A091901 Values of n for which sigma(n) < e^gamma * n * log(log(n)).

7, 11, 13, 14, 15, 17, 19, 21, 22, 23, 25, 26, 27, 28, 29, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 85, 86, 87, 88, 89

Offset: 1

Author

Eric W. Weisstein, Feb 09 2004

Keywords

• nonn
• easy

Comments

sigma(n) < e^gamma * n * log(log(n)) is "Robin's inequality" - see A067698. Sequence is cofinite if and only if the Riemann Hypothesis is true.

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.
• G. Caveney, J.-L. Nicolas and J. Sondow, On SA, CA, and GA numbers, Ramanujan J., 29 (2012), 359-384.
• Eric Weisstein's World of Mathematics, Robin's Theorem

Crossrefs

Cf. A067698.

Programs

Mathematica

Select[Range[100], DivisorSigma[1, #] < E^EulerGamma*#*Log[Log[#]] &] (* Jean-François Alcover, Oct 30 2012 *)

Formula

a(n) = n + 27 for n > 5039, if and only if the Riemann Hypothesis is true. - Charles R Greathouse IV, May 31 2011