A060895 a(n) = n^16 + 1.

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

Offset: 0

Author

N. J. A. Sloane, May 05 2001

Keywords

• nonn
• easy

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).

Programs

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 *)

PARI

a(n) = { n^16 + 1 } \\ Harry J. Smith, Jul 14 2009

Formula

G.f.: -(2*x^16 +65503*x^15 [phone]*x^14 [phone]*x^13 [phone]*x^12 [phone]*x^11 [phone]*x^10 [phone]*x^9 [phone]*x^8 [phone]*x^7 [phone]*x^6 [phone]*x^5 [phone]*x^4 [phone]*x^3 +65639*x^2 -15*x +1)/(x -1)^17. - Colin Barker, Oct 29 2012