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A105607
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Sylvester cyclotomic numbers for A002605.
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2
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Primitive parts of A002605.
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LINKS
| Eric Weisstein's World of Mathematics, Sylvester Cyclotomic Number.
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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 (rgwv(AT)rgwv.com), Aug 02 2005
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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] (from Robert G. Wilson v (rgwv(AT)rgwv.com), Aug 02 2005)
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CROSSREFS
| Cf. A002605, A105608, A105609.
Sequence in context: A065953 A118211 A050552 * A098239 A140257 A204546
Adjacent sequences: A105604 A105605 A105606 * A105608 A105609 A105610
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KEYWORD
| nonn
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Apr 15 2005
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EXTENSIONS
| More terms from David Wasserman (dwasserm(AT)earthlink.net), May 06 2008
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