A019320 Cyclotomic polynomials at x=2.

2, 1, 3, 7, 5, 31, 3, 127, 17, 73, 11, 2047, 13, 8191, 43, 151, 257, 131071, 57, 524287, 205, 2359, 683, 8388607, 241, 1082401, 2731, 262657, 3277, 536870911, 331, 2147483647, 65537, 599479, 43691, 8727391, 4033, 137438953471, 174763, 9588151, 61681

Offset: 0

Author

Simon Plouffe

Keywords

• nonn

Links

• T. D. Noe, Table of n, a(n) for n = 0..1000
• Joerg Arndt, Matters Computational (The Fxtbook)
• Index entries for cyclotomic polynomials, values at X

Crossrefs

a(n) = A063696(n) - A063698(n) for up to n=104.

Same sequence in binary: A063672.

Cf. A054432, A020501, A034268.

Programs

Maple

with(numtheory,cyclotomic); f := n->subs(x=2,cyclotomic(n,x)); seq(f(i),i=0..64);

Mathematica

Join[{2}, Table[Cyclotomic[n, 2], {n, 1, 40}]] (* Jean-François Alcover, Jun 14 2013 *)

PARI

vector(20,n,polcyclo(n,2)) \\ Charles R Greathouse IV, May 18 2011

Formula

(lcm_{k=1..n} (2^k - 1))/lcm_{k=1..n-1} (2^k - 1), n > 1. - Vladeta Jovovic, Jan 20 2002

Let b(1) = 1 and b(n+1) = lcm(b(n), 2^n-1) then Phi(n,2) = b(n+1)/b(n) = a(n). - Thomas Ordowski, May 08 2013

a(0) = 2; for n > 0, a(n) = (2^n-1)/gcd(a(0)*a(1)*...*a(n-1), 2^n-1). - Thomas Ordowski, May 11 2013