A105607 Sylvester cyclotomic numbers for A002605.

1, 2, 6, 8, 44, 10, 328, 56, 408, 76, 18272, 52, 136384, 568, 3856, 3104, 7598336, 424, 56714752, 2896, 215104, 31648, 3159738368, 3088, 536013824, 236224, 71910912, 161344, 1313964867584, 2320, 9807567290368, 9634304, 667730944, 13160704, 37860806656, 172864, 4078438577864704, 98232832, 37201186816, 9584896

Offset

1,2

Comments

Primitive parts of A002605.

Links

Table of n, a(n) for n=1..40.

Eric Weisstein's World of Mathematics, Sylvester Cyclotomic Number.

Formula

a(n) = A002605(n)/A105606(n); a(n) = product{k=1..n-1, if(gcd(n, k)=1, (1+sqrt(3))-(1-sqrt(3))*exp(2*Pi*I*k/n), 1)}, I=sqrt(-1). - Robert G. Wilson v, Aug 02 2005

Mathematica

f[n_] := FullSimplify[ Expand[ Times @@ ((1+Sqrt[3])-(1-Sqrt[3])*Exp[2Pi*I*Select[Range[n], GCD[ #, n] == 1 &]/n])]]; Table[ f[n], {n, 2, 32] (* Robert G. Wilson v, Aug 02 2005 *)

Crossrefs

Cf. A002605, A105608, A105609.

Sequence in context: A371832 A118211 A050552 * A098239 A140257 A361427

Adjacent sequences: A105604 A105605 A105606 * A105608 A105609 A105610

Keyword

nonn

Author

Paul Barry, Apr 15 2005

Extensions

More terms from David Wasserman, May 06 2008

Status

approved