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A329006 a(n) = p(1,n), where p(x,n) is the strong divisibility sequence of polynomials based on sqrt(2) as in A327320. 3
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified November 30 21:57 EST 2022. Contains 358453 sequences. (Running on oeis4.)