A056056 Square root of largest square dividing n-th central binomial coefficient.

1, 1, 1, 1, 1, 2, 1, 1, 3, 6, 1, 2, 2, 2, 3, 3, 1, 2, 1, 2, 2, 2, 1, 2, 10, 10, 30, 30, 6, 12, 3, 3, 3, 6, 5, 10, 10, 10, 3, 6, 2, 2, 2, 2, 30, 60, 15, 30, 42, 42, 42, 42, 14, 28, 2, 2, 2, 4, 2, 4, 4, 4, 21, 21, 7, 14, 7, 14, 6, 6, 1, 2, 2, 2, 10, 10, 70, 140, 7, 14, 126, 126, 6, 6, 30, 60

Offset

1,6

Links

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

Formula

a(n) = A000188(A001405(n)).

Mathematica

Table[Sqrt@ Max@ Select[Divisors@ Binomial[n, Floor[n/2]], IntegerQ@ Sqrt@ # &], {n, 0, 86}] (* Michael De Vlieger, Jul 04 2016 *)
a[n_] := Times @@ (First[#]^Floor[Last[#]/2] & /@ FactorInteger[Binomial[n, Floor[n/2]]]); Array[a, 100] (* Amiram Eldar, Sep 06 2020 *)

Prog

(PARI) a(n) = b = binomial(n, n\2); sqrtint(b/core(b)); \\ Michel Marcus, Dec 10 2013

Crossrefs

Cf. A001405, A000188, A008833, A007913, A055229, A055231, A056057, A056058, A056059, A056060, A056061.

Sequence in context: A293785 A156881 A056646 * A136462 A320574 A060517

Adjacent sequences: A056053 A056054 A056055 * A056057 A056058 A056059

Keyword

nonn

Author

Labos Elemer, Jul 26 2000

Status

approved