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

2, 1, 22, 16, 316, 10, 4264, 184, 2584, 124, 756064, 148, 10050496, 1624, 19216, 31264, 1775616256, 2152, 23600633344, 25936, 3343936, 285856, 4169384372224, 29968, 175371467776, 3798976, 12957013504, 4580416

Offset: 1

Author

Miklos Kristof, Apr 03 2007

Keywords

• nonn

Examples

			F(12)=a(1)*a(2)*a(3)*a(4)*a(6)*a(12)=2*1*22*16*10*148=1041920
F(9)=a(2)*a(6)*a(18)= 1*10*2152=21520
L(12)=a(8)*a(24)=184*29968=5514112
L(21)=a(1)*a(3)*a(7)*a(21)=2*22*4264*3343936=627375896576
		

Crossrefs

Cf. A072270, A083099, A127226.

Programs

Maple

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);

Formula

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);