A127607 - OEIS

%I #6 Mar 31 2012 14:39:58

%S 2,1,22,16,316,10,4264,184,2584,124,756064,148,10050496,1624,19216,

%T 31264,1775616256,2152,23600633344,25936,3343936,285856,4169384372224,

%U 29968,175371467776,3798976,12957013504,4580416

%N Sequence arising from the factorization of F(n)= A083099(n) and L(n)= A127226(n).

%F a(n)= (sqrt(7)-1)^degree(cyclotomic(n,x),x)*cyclotomic(n,(4+sqrt(7)/3) L(n)=6*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);

%e F(12)=a(1)*a(2)*a(3)*a(4)*a(6)*a(12)=2*1*22*16*10*148=1041920

%e F(9)=a(2)*a(6)*a(18)= 1*10*2152=21520

%e L(12)=a(8)*a(24)=184*29968=5514112

%e L(21)=a(1)*a(3)*a(7)*a(21)=2*22*4264*3343936=627375896576

%p with(numtheory): a[1]:=2:a[2]:=1:for n from 3 to 60 do a[n]:=round(evalf((sqrt(7)-1)^degree(cyclotomic(n, x), x) *cyclotomic(n, (4+sqrt(7))/3), 30)) od: seq(a[n], n=1..60);

%Y Cf. A072270, A083099, A127226.

%K nonn

%O 1,1

%A _Miklos Kristof_, Apr 03 2007