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.
%I A051764 #34 Feb 16 2025 08:32:41
%S A051764 0,0,1,0,1,0,1,1,1,1,1,0,1,1,2,1,1,0,1,1,2,1,1,1,1,1,2,2,1,0,1,2,2,1,
%T A051764 2,1,1,1,2,1,1,0,1,2,2,1,1,2,1,1,2,2,1,1,2,2,2,1,1,1,1,1,3,2,2,1,1,2,
%U A051764 2,1,1,2,1,1,2,2,2,1,1,2,2,1,1,1,2,1,2,3,1,1,2,2,2,1,2,2,1,1,3,1,1,1,1,3,3
%N A051764 Number of torus knots with n crossings.
%H A051764 Alois P. Heinz, <a href="/A051764/b051764.txt">Table of n, a(n) for n = 1..20000</a>
%H A051764 D. Bar-Natan, <a href="http://katlas.org/wiki/36_Torus_Knots">36 Torus Knots(with up to 36 crossings)</a>
%H A051764 Jim Hoste, Morwen Thistlethwaite, Jeff Weeks, <a href="http://dx.doi.org/10.1007/BF03025227">The First 1,701,936 Knots</a>, Math. Intell., 20, 33-48, Fall 1998.
%H A051764 Andrei Malyutin, <a href="https://arxiv.org/abs/1612.03368">On the question of genericity of hyperbolic knots</a>, arXiv preprint arXiv:1612.03368 [math.GT], 2016.
%H A051764 Kunio Murasugi, <a href="https://doi.org/10.1090/S0002-9947-1991-1000333-3">On the braid index of alternating links</a>, Trans. Amer. Math. Soc. 326 (1991), 237-260.
%H A051764 R. G. Scharein, <a href="https://knotplot.com/knot-theory/torus_xing.html">Torus knots and links by crossing number</a>
%H A051764 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HyperbolicKnot.html">Hyperbolic Knot</a>
%H A051764 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Knot.html">Knot</a>
%H A051764 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/TorusKnot.html">Torus Knot</a>
%F A051764 a(n) = cardinality of the set {k| sqrt(n) < k <= n and gcd(k, 1+n/k) = 1}; see Murasugi article. - _Hermann Gruber_, Mar 05 2003
%p A051764 a:= n-> nops(select(k-> n<k^2 and igcd(k, 1+n/k)=1, numtheory[divisors](n))):
%p A051764 seq(a(n), n=1..100); # _Alois P. Heinz_, Apr 25 2012
%t A051764 a[n_] := (r = Reduce[Sqrt[n] < k <= n && GCD[k, 1 + n/k] == 1, k, Integers]; Which[r === False, 0, r[[0]] === Equal, 1, True, Length[r]]); Table[a[n], {n, 1, 105}] (* _Jean-François Alcover_, Jan 16 2013 *)
%o A051764 (PARI) a(n)=my(t=sqrtint(n));sumdiv(n,k,k>t && gcd(k,n/k+1)==1) \\ _Charles R Greathouse IV_, Apr 26 2012
%K A051764 nonn,nice
%O A051764 1,15
%A A051764 _Eric W. Weisstein_