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A019320 Cyclotomic polynomials at x=2.

%I A019320 #46 Mar 08 2022 08:17:18
%S A019320 2,1,3,7,5,31,3,127,17,73,11,2047,13,8191,43,151,257,131071,57,524287,
%T A019320 205,2359,683,8388607,241,1082401,2731,262657,3277,536870911,331,
%U A019320 2147483647,65537,599479,43691,8727391,4033,137438953471,174763,9588151,61681
%N A019320 Cyclotomic polynomials at x=2.
%H A019320 T. D. Noe, <a href="/A019320/b019320.txt">Table of n, a(n) for n = 0..1000</a>
%H A019320 Joerg Arndt, <a href="http://www.jjj.de/fxt/#fxtbook">Matters Computational (The Fxtbook)</a>
%H A019320 <a href="/index/Cy#CyclotomicPolynomialsValuesAtX">Index entries for cyclotomic polynomials, values at X</a>
%F A019320 (lcm_{k=1..n} (2^k - 1))/lcm_{k=1..n-1} (2^k - 1), n > 1. - _Vladeta Jovovic_, Jan 20 2002
%F A019320 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
%F A019320 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
%p A019320 with(numtheory,cyclotomic); f := n->subs(x=2,cyclotomic(n,x)); seq(f(i),i=0..64);
%t A019320 Join[{2}, Table[Cyclotomic[n, 2], {n, 1, 40}]] (* _Jean-François Alcover_, Jun 14 2013 *)
%o A019320 (PARI) vector(20,n,polcyclo(n,2)) \\ _Charles R Greathouse IV_, May 18 2011
%Y A019320 a(n) = A063696(n) - A063698(n) for up to n=104.
%Y A019320 Same sequence in binary: A063672.
%Y A019320 Cf. A054432, A020501, A034268.
%K A019320 nonn
%O A019320 0,1
%A A019320 _Simon Plouffe_