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
KEYWORD
nonn,changed
AUTHOR
Eric W. Weisstein, Jan 14 2005
EXTENSIONS
New definition by Charles R Greathouse IV, Mar 24 2014
STATUS
approved