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

1,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

A. Stoimenow, Square numbers, spanning trees and invariants of rational knots (2000)

Formula

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

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 *)

Prog

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

Crossrefs

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

Sequence in context: A177862 A066981 A130043 * A178993 A193768 A361784

Adjacent sequences: A089263 A089264 A089265 * A089267 A089268 A089269

Keyword

nonn,easy,nice

Author

Ralf Stephan, Oct 30 2003

Status

approved