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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.

%I A329006 #6 Nov 23 2019 13:40:23
%S A329006 1,5,7,85,341,455,5461,21845,9709,349525,1398101,1864135,22369621,
%T A329006 89478485,119304647,1431655765,5726623061,2545165805,91625968981,
%U A329006 366503875925,488671834567,5864062014805,23456248059221,31274997412295,375299968947541,15011998757901653
%N A329006 a(n) = p(1,n), where p(x,n) is the strong divisibility sequence of polynomials based on sqrt(2) as in A327320.
%C A329006 a(n) is a strong divisibility sequence; i.e., gcd(a(h),a(k)) = a(gcd(h,k)).
%e A329006 See Example in A327320.
%t A329006 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];
%t A329006 r = Sqrt[2]; f[x_, n_] := c[Factor[Expand[(r x + r)^n - (r x - 1/r)^n]]];
%t A329006 Flatten[Table[CoefficientList[f[x, n], x], {n, 1, 12}]];  (* A327320 *)
%t A329006 Table[f[x, n] /. x -> 0, {n, 1, 30}]   (* A329005 *)
%t A329006 Table[f[x, n] /. x -> 1, {n, 1, 30}]   (* A329006 *)
%t A329006 Table[f[x, n] /. x -> 2, {n, 1, 30}]   (* A329007 *)
%t A329006 (* _Peter J. C. Moses_, Nov 01 2019 *)
%Y A329006 Cf. A327320, A329005, A329007.
%K A329006 nonn
%O A329006 1,2
%A A329006 _Clark Kimberling_, Nov 08 2019