A056057 The largest square which divides n-th central binomial coefficient.

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

Offset: 1

Author

Labos Elemer, Jul 26 2000

Keywords

• nonn

Links

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

Crossrefs

Cf. A001405, A000188, A008833, A007913, A055229, A055231, A046098, A034974.

Cf. A056056, A056058, A056059, A056060, A056061.

Programs

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 *)

Formula

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

a(A046098(n)) = 1.