A102562 Numbers k such that the cyclic group of order k is not a Hajós group.

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

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).

Christophe Cordero, Factorizations of Cyclic Groups and Bayonet Codes, arXiv:2301.13566 [math.CO], 2023, p. 4.

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 and 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).

Marie Lhuissier, Canons rythmiques mosaïques, Images des Mathématiques, CNRS, 2023.

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 * A357460 A216426 A308053

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