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A127607 Sequence arising from the factorization of F(n)= A083099(n) and L(n)= A127226(n).

%I A127607 #6 Mar 31 2012 14:39:58
%S A127607 2,1,22,16,316,10,4264,184,2584,124,756064,148,10050496,1624,19216,
%T A127607 31264,1775616256,2152,23600633344,25936,3343936,285856,4169384372224,
%U A127607 29968,175371467776,3798976,12957013504,4580416
%N A127607 Sequence arising from the factorization of F(n)= A083099(n) and L(n)= A127226(n).
%F A127607 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 A127607 F(12)=a(1)*a(2)*a(3)*a(4)*a(6)*a(12)=2*1*22*16*10*148=1041920
%e A127607 F(9)=a(2)*a(6)*a(18)= 1*10*2152=21520
%e A127607 L(12)=a(8)*a(24)=184*29968=5514112
%e A127607 L(21)=a(1)*a(3)*a(7)*a(21)=2*22*4264*3343936=627375896576
%p A127607 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 A127607 Cf. A072270, A083099, A127226.
%K A127607 nonn
%O A127607 1,1
%A A127607 _Miklos Kristof_, Apr 03 2007