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A105608
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Sylvester dividends for A002605.
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2
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1, 1, 1, 2, 1, 12, 1, 16, 6, 88, 1, 960, 1, 656, 264, 896, 1, 48960, 1, 53504, 1968, 36544, 1, 2795520, 44, 272768, 2448, 2980864, 1, 1547335680, 1, 2781184, 109632, 15196672, 14432, 8635760640, 1, 113429504, 818304, 8677064704, 1, 4808968273920, 1, 9252356096, 415337472, 6319476736, 1, 26795484119040, 328, 3584860454912
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,4
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LINKS
| Eric Weisstein's World of Mathematics, Sylvester Cyclotomic Number.
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FORMULA
| a(n)=A002605(n)/A105607(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)
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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. A105607, A105609.
Sequence in context: A128247 A161150 A163088 * A051190 A072512 A118588
Adjacent sequences: A105605 A105606 A105607 * A105609 A105610 A105611
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KEYWORD
| easy,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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