A089266 Rational knots of determinant 2n+1, counting chiral pairs twice.

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, 22, 20, 30, 31, 20, 26, 34, 24, 36, 37, 22, 32, 40, 28, 42, 34, 30, 45, 38, 32, 38, 49, 32, 51, 52, 28, 54, 55, 38, 57, 46, 38, 50, 56, 42, 51, 64, 44, 66, 56

Offset: 1

Author

Ralf Stephan, Oct 30 2003

Keywords

• nonn
• easy
• nice

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• A. Stoimenow, Square numbers, spanning trees and invariants of rational knots (2000)

Crossrefs

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

Programs

Mathematica

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 *)

PARI

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

Formula

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