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

Author

Paul Barry, Apr 15 2005

Keywords

• easy
• nonn

Links

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

Crossrefs

Cf. A105607, A105609.

Programs

Mathematica

f[n_] := FullSimplify[ Expand[ Times @@ ((1+Sqrt[3])-(1-Sqrt[3])*Exp[2Pi*I*Select[Range[n-1], GCD[ #, n] > 1 &]/n])]]; Table[ f[n], {n, 1, 32}] (* Robert G. Wilson v, Aug 02 2005 *)

Formula

a(n) = A002605(n)/A105607(n); a(n) = Product_{k=1..n-1, gcd(n, k)>1} (1+sqrt(3))-(1-sqrt(3))*exp(2*Pi*i*k/n), i = sqrt(-1).

Extensions

More terms from David Wasserman, May 06 2008