This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
Triangle begins: n\k| 0 1 2 3 4 ---+------------------- 3 | 0 1 4 | 0 1 5 | 0 1 1 6 | 0 3 7 | 0 3 3 1 8 | 0 9 11 1 9 | 0 17 22 9 1
Let K denote a prime knot in Alexander-Briggs notation, and let sigma(K) and u(K) denote the signature and the unknotting number of the knot K, respectively. The following table gives some of the first prime knots with the property u(K) = (1/2)*abs(sigma(K)). ================================================================== | K | 3_1 | 5_1 | 5_2 | 6_2 | 7_1 | 7_2 | 7_5 | 7_6 | 8_2 | -----------+-----+-----+-----+-----+-----+-----+-----+-----+-----+ | sigma(K) | -2 | -4 | -2 | -2 | -6 | -2 | -4 | -2 | -4 | -----------+-----+-----+-----+-----+-----+-----+-----+-----+-----+ | u(K) | 1 | 2 | 1 | 1 | 3 | 1 | 2 | 1 | 2 | ==================================================================
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 *)
a(n)=(eulerphi(2*n+1)+2^omega(2*n+1))/2
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