

A089266


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


1



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
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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}] (* JeanFrançois 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 A205791
Adjacent sequences: A089263 A089264 A089265 * A089267 A089268 A089269


KEYWORD

nonn,easy,nice


AUTHOR

Ralf Stephan, Oct 30 2003


STATUS

approved



