login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A329005 a(n) = p(0,n), where p(x,n) is the strong divisibility sequence of polynomials based on sqrt(2) as in A327320. 3
1, 1, 1, 5, 11, 7, 43, 85, 19, 341, 683, 455, 2731, 5461, 3641, 21845, 43691, 9709, 174763, 349525, 233017, 1398101, 2796203, 1864135, 11184811, 22369621, 1657009, 89478485, 178956971, 119304647, 715827883, 1431655765, 954437177, 5726623061, 11453246123 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

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..35.

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, A329006, A329007.

Sequence in context: A068419 A226586 A358613 * A290195 A082952 A113964

Adjacent sequences: A329002 A329003 A329004 * A329006 A329007 A329008

KEYWORD

nonn

AUTHOR

Clark Kimberling, Nov 08 2019

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified January 29 10:31 EST 2023. Contains 359916 sequences. (Running on oeis4.)