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A051764
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Number of torus knots with n crossings.
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5
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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
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OFFSET
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1,15
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LINKS
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Eric Weisstein's World of Mathematics, Knot
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FORMULA
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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
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MAPLE
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with(numtheory):
a:= n-> nops (select (k-> is (sqrt(n)<k and igcd(k, 1+n/k)=1), divisors(n))):
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MATHEMATICA
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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 *)
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PROG
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CROSSREFS
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KEYWORD
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nonn,nice
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AUTHOR
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STATUS
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approved
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