

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
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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



