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Cyclotomic polynomials at x=8.
6

%I #23 Feb 26 2024 09:14:33

%S 8,7,9,73,65,4681,57,299593,4097,262657,3641,1227133513,4033,

%T 78536544841,233017,14709241,16777217,321685687669321,261633,

%U 20587884010836553,16519105,60247241209,954437177,84327972908386521673,16773121,1152956690052710401,61083979321

%N Cyclotomic polynomials at x=8.

%H Paolo Xausa, <a href="/A019326/b019326.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Cy#CyclotomicPolynomialsValuesAtX">Index entries for cyclotomic polynomials, values at X</a>

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

%t Join[{8}, Cyclotomic[Range[50], 8]] (* _Paolo Xausa_, Feb 26 2024 *)

%o (Python)

%o from sympy.polys.specialpolys import cyclotomic_poly

%o def a(n): return 8 if n == 0 else cyclotomic_poly(n, x=8)

%o print([a(n) for n in range(27)]) # _Michael S. Branicky_, Aug 07 2021

%o (PARI) a(n) = if (n==0, 8, polcyclo(n, 8)); \\ _Michel Marcus_, Aug 07 2021

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

%K nonn

%O 0,1

%A _Simon Plouffe_