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A105608 Sylvester dividends for A002605. 2
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; text; internal format)
OFFSET

1,4

LINKS

Table of n, a(n) for n=1..50.

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

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),

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. A105607, A105609.

Sequence in context: A128247 A161150 A163088 * A051190 A072512 A271531

Adjacent sequences:  A105605 A105606 A105607 * A105609 A105610 A105611

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Apr 15 2005

EXTENSIONS

More terms from David Wasserman, May 06 2008

STATUS

approved

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Last modified June 17 17:05 EDT 2021. Contains 345085 sequences. (Running on oeis4.)