A329006 a(n) = p(1,n), where p(x,n) is the strong divisibility sequence of polynomials based on sqrt(2) as in A327320.

1, 5, 7, 85, 341, 455, 5461, 21845, 9709, 349525, 1398101, 1864135, 22369621, 89478485, 119304647, 1431655765, 5726623061, 2545165805, 91625968981, 366503875925, 488671834567, 5864062014805, 23456248059221, 31274997412295, 375299968947541, 15011998757901653

Offset

1,2

Comments

a(n) is a strong divisibility sequence; i.e., gcd(a(h),a(k)) = a(gcd(h,k)).

Links

Table of n, a(n) for n=1..26.

Example

See Example in A327320.

Mathematica

c[poly_] := If[Head[poly] === Times, Times @@ DeleteCases[(#1 (Boole[MemberQ[#1, x] || MemberQ[#1, y] || MemberQ[#1, z]] &) /@Variables /@ #1 &)[List @@ poly], 0], poly];
r = Sqrt[2]; f[x_, n_] := c[Factor[Expand[(r x + r)^n - (r x - 1/r)^n]]];
Flatten[Table[CoefficientList[f[x, n], x], {n, 1, 12}]];  (* A327320 *)
Table[f[x, n] /. x -> 0, {n, 1, 30}]   (* A329005 *)
Table[f[x, n] /. x -> 1, {n, 1, 30}]   (* A329006 *)
Table[f[x, n] /. x -> 2, {n, 1, 30}]   (* A329007 *)
(* Peter J. C. Moses, Nov 01 2019 *)

Crossrefs

Cf. A327320, A329005, A329007.

Sequence in context: A062583 A196139 A165784 * A176619 A230379 A292847

Adjacent sequences: A329003 A329004 A329005 * A329007 A329008 A329009

Keyword

nonn

Author

Clark Kimberling, Nov 08 2019

Status

approved