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A056057 The largest square which divides n-th central binomial coefficient. 10
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,6

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = A008833(A001405(n)).

a(A046098(n)) = 1.

MATHEMATICA

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 *)

CROSSREFS

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

KEYWORD

nonn

AUTHOR

Labos Elemer, Jul 26 2000

STATUS

approved

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Last modified August 4 12:27 EDT 2021. Contains 346447 sequences. (Running on oeis4.)