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Rational knots of determinant 2n+1, counting chiral pairs twice.
1

%I #13 Oct 11 2013 16:49:15

%S 2,3,4,4,6,7,6,9,10,8,12,11,10,15,16,12,14,19,14,21,22,14,24,22,18,27,

%T 22,20,30,31,20,26,34,24,36,37,22,32,40,28,42,34,30,45,38,32,38,49,32,

%U 51,52,28,54,55,38,57,46,38,50,56,42,51,64,44,66,56

%N Rational knots of determinant 2n+1, counting chiral pairs twice.

%H Vincenzo Librandi, <a href="/A089266/b089266.txt">Table of n, a(n) for n = 1..1000</a>

%H A. Stoimenow, <a href="http://arxiv.org/abs/math.GT/0003172">Square numbers, spanning trees and invariants of rational knots</a> (2000)

%F a(n) = 1/2 * (A037225(n) + A034444(2*n+1)).

%t a[n_] := (EulerPhi[2*n+1] + 2^PrimeNu[2*n+1])/2; Table[a[n], {n, 1, 66}] (* _Jean-François Alcover_, Oct 11 2013, after Pari *)

%o (PARI) a(n)=(eulerphi(2*n+1)+2^omega(2*n+1))/2

%Y Cf. A078477, A078478, A018240, A051449, A051766.

%K nonn,easy,nice

%O 1,1

%A _Ralf Stephan_, Oct 30 2003