A105608 Sylvester dividends for A002605.

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

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