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A105607
Sylvester cyclotomic numbers for A002605.
2
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
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
KEYWORD
nonn
AUTHOR
Paul Barry, Apr 15 2005
EXTENSIONS
More terms from David Wasserman, May 06 2008
STATUS
approved