A105609 -id:A105609 - cp's OEIS frontend

A105607 Sylvester cyclotomic numbers for A002605.

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

Offset: 1

Paul Barry, Apr 15 2005

nonn

Primitive parts of A002605.

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

Cf. A002605, A105608, A105609.

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 *)

a(n) = A002605(n)/A105606(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). - Robert G. Wilson v, Aug 02 2005

More terms from David Wasserman, May 06 2008

A105608 Sylvester dividends for A002605.

Original entry on oeis.org

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

Paul Barry, Apr 15 2005

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

Cf. A105607, A105609.

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 *)

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).

More terms from David Wasserman, May 06 2008

cp's OEIS Frontend

A105607 Sylvester cyclotomic numbers for A002605.

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