A136268 Cyclic p-roots of prime lengths p(n).

2, 6, 70, 924, 184756, 2704156, 601080390, 9075135300, 2104098963720, 7648690600760440, 118264581564861424, 442512540276836779204, 107507208733336176461620, 1678910486211891090247320, 410795449442059149332177040

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