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). (Formerly M2934 N1180)

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

Offset

1,1

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

Table of n, a(n) for n=1..21.

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.

Sequence in context: A078162 A348002 A211774 * A228251 A348200 A218092

Adjacent sequences: A002494 A002495 A002496 * A002498 A002499 A002500

Keyword

nonn,easy,nice

Author

N. J. A. Sloane

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

Status

approved