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A136268 Cyclic p-roots of prime lengths p(n). 0
2, 6, 70, 924, 184756, 2704156, 601080390, 9075135300, 2104098963720, 7648690600760440, 118264581564861424, 442512540276836779204, 107507208733336176461620, 1678910486211891090247320, 410795449442059149332177040 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

In this paper it is proved, that for every prime number p, the set of cyclic p-roots in C^p is finite. Moreover the number of cyclic p-roots counted with multiplicity is equal to (2p-2)!/(p-1)!^2. In particular, the number of complex circulant Hadamard matrices of size p, with diagonal entries equal to 1, is less than or equal to (2p-2)!/(p-1)!^2.

LINKS

Table of n, a(n) for n=1..15.

Uffe Haagerup, Cyclic p-roots of prime lengths p and related complex Hadamard matrices, arXiv:0803.2629 Mar 19, 2008.

FORMULA

a(n) = (2*p_n - 2)!/(p_n - 1)!^2 where p_n = prime(n) = A000040(n). a(n) = A000142(2*A000040(n)-2)/((A000142(A000040(n)-1)^2).

CROSSREFS

Cf. A000040, A000142.

Sequence in context: A219037 A156458 A244494 * A030242 A037293 A129785

Adjacent sequences: A136265 A136266 A136267 * A136269 A136270 A136271

KEYWORD

easy,nonn

AUTHOR

Jonathan Vos Post, Mar 18 2008

STATUS

approved

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Last modified December 8 12:39 EST 2022. Contains 358693 sequences. (Running on oeis4.)