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A056057
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The largest square which divides n-th central binomial coefficient.
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10
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1, 1, 1, 1, 1, 4, 1, 1, 9, 36, 1, 4, 4, 4, 9, 9, 1, 4, 1, 4, 4, 4, 1, 4, 100, 100, 900, 900, 36, 144, 9, 9, 9, 36, 25, 100, 100, 100, 9, 36, 4, 4, 4, 4, 900, 3600, 225, 900, 1764, 1764, 1764, 1764, 196, 784, 4, 4, 4, 16, 4, 16, 16, 16, 441, 441, 49, 196, 49, 196, 36, 36, 1, 4
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OFFSET
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1,6
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LINKS
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Amiram Eldar, Table of n, a(n) for n = 1..10000
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FORMULA
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a(n) = A008833(A001405(n)).
a(A046098(n)) = 1.
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MATHEMATICA
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Table[First@ Select[Reverse@ Divisors@ Binomial[n, Floor[n/2]], IntegerQ@ Sqrt@ # &], {n, 72}] (* Michael De Vlieger, Feb 18 2017 *)
a[n_] := Times @@ (First[#]^(2*Floor[Last[#]/2]) & /@ FactorInteger[Binomial[n, Floor[n/2]]]); Array[a, 100] (* Amiram Eldar, Sep 06 2020 *)
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CROSSREFS
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Cf. A001405, A000188, A008833, A007913, A055229, A055231, A046098, A034974.
Cf. A056056, A056058, A056059, A056060, A056061.
Sequence in context: A219207 A157108 A056647 * A226234 A185027 A016520
Adjacent sequences: A056054 A056055 A056056 * A056058 A056059 A056060
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KEYWORD
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nonn
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AUTHOR
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Labos Elemer, Jul 26 2000
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STATUS
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approved
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