OFFSET
1,1
FORMULA
(sqrt(3)-1)^degree(cyclotomic(n,x),x)*cyclotomic(n,2+sqrt(3)) L(n)=2*F(n-1)+F(n+1) F(2n)=Product(d|2n) a(d), F(2n+1)=Product(d|2n+1) a(2d). L(2n+1)=Product(d|2n+1, a(d)), for k>0: L(2^k*(2n+1))=Product(d|2n+1, a(2^(k+1)*d)). for odd prime p, a(p)=L(p)/2, a(2p)=f(p) a(1)=2, a(2)=1; a(2^(k+1))=L(2^k);
EXAMPLE
F(12)=a(1)*a(2)*a(3)*a(4)*a(6)*a(12)=2*1*10*8*6*52=49920
F(9)=a(2)*a(6)*a(18)= 1*6*408=2448
L(12)=a(8)*a(24)=56*3088=172928
L(21)=a(1)*a(3)*a(7)*a(21)=2*10*568*129088=1466439680
MAPLE
with(numtheory): a[1]:=2:a[2]:=1:for n from 3 to 60 do a[n]:=round(evalf((sqrt(3)-1)^degree(cyclotomic(n, x), x)*cyclotomic(n, 2+sqrt(3)), 30)) od: seq(a[n], n=1..60);
CROSSREFS
KEYWORD
nonn
AUTHOR
Miklos Kristof, Mar 26 2007
STATUS
approved