A019326 Cyclotomic polynomials at x=8.

8, 7, 9, 73, 65, 4681, 57, 299593, 4097, 262657, 3641, 1227133513, 4033, 78536544841, 233017, 14709241, 16777217, 321685687669321, 261633, 20587884010836553, 16519105, 60247241209, 954437177, 84327972908386521673, 16773121, 1152956690052710401, 61083979321

Offset: 0

Author

Simon Plouffe

Keywords

• nonn

Links

• Paolo Xausa, Table of n, a(n) for n = 0..1000
• Index entries for cyclotomic polynomials, values at X

Crossrefs

Cf. A020500 (x = 1), A019320-A019331 (x = 2..13).

Programs

Maple

with(numtheory,cyclotomic); f := n->subs(x=8,cyclotomic(n,x)); seq(f(i),i=0..64);

Mathematica

Join[{8}, Cyclotomic[Range[50], 8]] (* Paolo Xausa, Feb 26 2024 *)

PARI

a(n) = if (n==0, 8, polcyclo(n, 8)); \\ Michel Marcus, Aug 07 2021

Python

from sympy.polys.specialpolys import cyclotomic_poly
def a(n): return 8 if n == 0 else cyclotomic_poly(n, x=8)
print([a(n) for n in range(27)]) # Michael S. Branicky, Aug 07 2021