A279702 a(n) = floor( exp(gamma) k log log k ) - sigma(k), where gamma is Euler's constant (A001620) and sigma(k) is sum of divisors of k (A000203), the n-th colossally abundant number (A004490).

-5, -6, -9, -18, -26, -34, -123, -107, 3953, 90021, 203866, 678250, 3860926, 62168609, 1022130830, 22777519100, 46323907000, 1499885420000, 47625567000000, 318447820000000, 974228630000000, 36070436000000000

Offset: 2

Author

Gene Ward Smith, Dec 17 2016

Keywords

• sign

Comments

By Robin's theorem, if the Riemann hypothesis is true the only negative values this sequence attains are the first eight terms; if it is false, it becomes negative again somewhere farther on. Briggs conjectured, in effect, that this sequence is asymptotic to C k / sqrt(log(k)) for some constant C.

References

• G. Robin, Grandes valeurs de la fonction somme des diviseurs et hypothese de Riemann, J. Math. Pures Appl. 63 (1984), 187-213.

Links

• Keith Briggs, Abundant numbers and the Riemann Hypothesis, Experimental Math., Vol. 16 (2006), p. 251-256.

Crossrefs

Cf. A004490, A058209.