A060895 n^16 + 1.

1, 2, 65537, 43046722, 4294967297, 152587890626, 2821109907457, 33232930569602, 281474976710657, 1853020188851842, 10000000000000001, 45949729863572162, 184884258895036417, 665416609183179842, 2177953337809371137, 6568408355712890626

Offset

0,2

Comments

a(n) = Phi_32(n) where Phi_k is the k-th cyclotomic polynomial.

Links

Harry J. Smith, Table of n, a(n) for n = 0..1000

Hisanori Mishima, Factorizations of many number sequences

Index to values of cyclotomic polynomials of integer argument

Index entries for linear recurrences with constant coefficients, signature (17,-136,680,-2380,6188,-12376,19448,-24310,24310,-19448,12376,-6188,2380,-680,136,-17,1).

Formula

G.f.: -(2*x^16 +65503*x^15 +41932865*x^14 +3572084695*x^13 +85383240369*x^12 +782115513931*x^11 +3207483186165*x^10 +6382798914035*x^9 +6382798938345*x^8 +3207483166717*x^7 +782115526307*x^6 +85383234181*x^5 +3572087075*x^4 +41932185*x^3 +65639*x^2 -15*x +1)/(x -1)^17. [Colin Barker, Oct 29 2012]

Maple

A060895 := proc(n)
        numtheory[cyclotomic](32, n) ;
end proc:
seq(A060895(n), n=0..20) ; # R. J. Mathar, Feb 11 2014

Mathematica

Range[0, 25]^16 + 1 (* or *)
Cyclotomic[32, Range[0, 25]] (* Paolo Xausa, Feb 26 2024 *)

Prog

(PARI) { for (n=0, 1000, write("b060895.txt", n, " ", n^16 + 1); ) } \\ Harry J. Smith, Jul 14 2009

Crossrefs

Sequence in context: A052427 A051833 A213619 * A100266 A272137 A272248

Adjacent sequences: A060892 A060893 A060894 * A060896 A060897 A060898

Keyword

nonn,easy

Author

N. J. A. Sloane, May 05 2001

Status

approved