|
|
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)
|
|
1
|
|
|
3, 12, 60, 420, 4620, 60060, 180180, 360360, 6126120, 116396280, 2677114440, 77636318760, 2406725881560, 89048857617720, 3651003162326520, 156993135980040360, 313986271960080720, 14757354782123793840, 14757354782123793840, 782139803452561073520, 46146248403701103337680
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
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
|
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy,nice
|
|
AUTHOR
|
|
|
EXTENSIONS
|
a(16)-a(21) from the paper by Massias added by Amiram Eldar, Aug 23 2019
|
|
STATUS
|
approved
|
|
|
|