A002497 Numbers N in A002809 such that there is rho > 0 such that for all A > 0, A008475(A)-A008475(N) >= rho*log(A/N).

3, 12, 60, 420, 4620, 60060, 180180, 360360, 6126120, 116396280, 2677114440, 77636318760, 2406725881560, 89048857617720, 3651003162326520, 156993135980040360, 313986271960080720, 14757354782123793840, 14757354782123793840, 782139803452561073520, 46146248403701103337680

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy
• nice

Comments

The numbers contain the starred entries on pp. 187-190 of Nicolas. It is a subsequence of A002809 by selecting only elements of a set/property "G" (page 150). G contains all N such that a real, strictly positive rho exists such that for all strictly positive integers A we have l(A)-l(N) >= rho*log(A/N). The function l()=A008475() is defined on page 139. - R. J. Mathar, Mar 23 2012

These numbers were named superior l-composite numbers (nombres l-composes superieurs, the function l(n) is A002809) by Massias, in analogy to Ramanujan's superior highly composite numbers (A002201). Deléglise and Nicolas named these numbers l-superchampion numbers. They are used by Deléglise et al. in calculating values of Landau's function g(n) (A000793). - Amiram Eldar, Aug 23 2019

References

• N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Marc Deléglise and Jean-Louis Nicolas, The Landau function and the Riemann hypothesis, arXiv preprint, arXiv:1907.07664 [math.NT] (2019).
• Marc Deléglise, Jean-Louis Nicolas, and Paul Zimmermann, Landau's function for one million billions, Journal de théorie des nombres de Bordeaux, Vol. 20. No. 3 (2008), pp. 625-671.
• Jean-Pierre Massias, Majoration explicite de l'ordre maximum d'un élément du groupe symétrique, Annales de la Faculté des Sciences de Toulouse: Mathématiques, Vol. 6, No. 3-4 (1984), pp. 269-281.
• Jean-Louis Nicolas, Ordre maximum d'un élément du groupe S(n) des permutations et "highly composite numbers", Bull. Soc. Math. Française 97 (1969), 129-191.

Crossrefs

Cf. A000793, A002201, A002498, A002809, A008475.

Extensions

Edited by M. F. Hasler, Mar 29 2015

a(16)-a(21) from the paper by Massias added by Amiram Eldar, Aug 23 2019