login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A102562 Numbers n such that the cyclic group of order n is not a Hajós group. 1
72, 108, 120, 144, 168, 180, 200, 216, 240, 252, 264, 270, 280, 288, 300, 312, 324, 336, 360, 378, 392, 396, 400, 408, 420, 432, 440, 450, 456, 468, 480, 500, 504, 520, 528, 540, 552, 560, 576, 588, 594, 600, 612, 616, 624, 630, 648, 660, 672, 675, 680 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Old name was "Orders of non-Hajós groups".

REFERENCES

F. Le Lionnais, Les Nombres Remarquables, Paris, Hermann, 1983, p. 94.

LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Emmanuel Amiot, Structures, Algorithms and Algebraic Tools for Rhythmic Canons, Perspectives of New Music, 2012, LAMPS, Perpignan, France (see page 6).

Moreno Andreatta, De la conjecture de Minkowski aux canons rythmiques mosaïques, IRCAM, Paris, (see page 6).

Jeremy Kastine, Maximally Even Tilings, International Conference on Mathematics and Computation in Music (MCM 2019), Lecture Notes in Computer Science, Vol. 11502, Springer, Cham, 309-321.

Jeffrey C Lagarias, Yang Wang, Spectral Sets and Factorizations of Finite Abelian Groups, Journal of Functional Analysis, Volume 145, Issue 1, Apr 01 1997, pp. 73-98 (see page 88).

Eric Weisstein's World of Mathematics, Hajos Group

FORMULA

a(n) = n + O(n(log log n)^3/log n). - Charles R Greathouse IV, Mar 24 2014

PROG

(PARI) is(n)=my(f=vecsort(factor(n)[, 2])~); #f>1 && f!=[2, 2] && (#f>2 || f[1]>1) && (#f!=3 || f[2]>1 || f[3]>2) && f!=[1, 1, 1, 1] \\ Charles R Greathouse IV, Mar 24 2014

CROSSREFS

Sequence in context: A242186 A205189 A258695 * A216426 A308053 A307758

Adjacent sequences:  A102559 A102560 A102561 * A102563 A102564 A102565

KEYWORD

nonn

AUTHOR

Eric W. Weisstein, Jan 14 2005

EXTENSIONS

New definition by Charles R Greathouse IV, Mar 24 2014

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 25 19:05 EDT 2021. Contains 346291 sequences. (Running on oeis4.)