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A102562
Numbers k such that the cyclic group of order k 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
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
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
KEYWORD
nonn,changed
AUTHOR
Eric W. Weisstein, Jan 14 2005
EXTENSIONS
New definition by Charles R Greathouse IV, Mar 24 2014
STATUS
approved