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 A051764 Number of torus knots with n crossings. 4
 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, 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, 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,15 LINKS Alois P. Heinz, Table of n, a(n) for n = 1..10000 D. Bar-Natan, 36 Torus Knots(with up to 36 crossings) Jim Hoste, Morwen Thistlethwaite, Jeff Weeks, The First 1,701,936 Knots, Math. Intell., 20, 33-48, Fall 1998. Andrei Malyutin, On the question of genericity of hyperbolic knots, arXiv preprint arXiv:1612.03368 [math.GT], 2016. Kunio Murasugi, On the braid index of alternating links, Trans. Amer. Math. Soc. 326 (1991), 237-260. R. G. Scharein, Torus knots and links by crossing number Eric Weisstein's World of Mathematics, Hyperbolic Knot Eric Weisstein's World of Mathematics, Knot Eric Weisstein's World of Mathematics, Torus Knot FORMULA 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 MAPLE with(numtheory): a:= n-> nops (select (k-> is (sqrt(n)t && gcd(k, n/k+1)==1) \\ Charles R Greathouse IV, Apr 26 2012 CROSSREFS Sequence in context: A214438 A173432 A101675 * A268533 A275849 A025906 Adjacent sequences:  A051761 A051762 A051763 * A051765 A051766 A051767 KEYWORD nonn,nice AUTHOR STATUS approved

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Last modified December 8 14:38 EST 2019. Contains 329865 sequences. (Running on oeis4.)