A069113 Squarefree part of C(2n,n), the central binomial numbers: the smallest number such that a(n)*C(2n,n) is a square.

1, 2, 6, 5, 70, 7, 231, 858, 1430, 12155, 46189, 176358, 676039, 104006, 44574, 1077205, 66786710, 64822395, 90751353, 353452638, 3829070245, 134564468610, 526024740930, 2287064091, 35830670759, 71661341518, 281132955186, 2483341104143, 1912172650190110

Offset

0,2

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Formula

a(n) = A271187(2n,n). - Alois P. Heinz, Apr 01 2016

a(n) = A007913(A000984(n)). - Amiram Eldar, May 23 2022

Maple

a:= n-> mul(i[1]^irem(i[2], 2), i=ifactors(binomial(2*n, n))[2]):
seq(a(n), n=0..35);  # Alois P. Heinz, Apr 01 2016

Mathematica

a[n_] := Times @@ ((First[#]^Mod[Last[#], 2]) & /@ FactorInteger[Binomial[2*n, n]]); Array[a, 30, 0] (* Amiram Eldar, May 23 2022 *)

Prog

(PARI) for(n=1, 60, print1(core(binomial(2*n, n)), ", "))

Crossrefs

Cf. A000984, A007913, A271187.

May be the same as A085057.

Sequence in context: A358746 A175350 A085057 * A298329 A009462 A346712

Adjacent sequences: A069110 A069111 A069112 * A069114 A069115 A069116

Keyword

easy,nonn

Author

Benoit Cloitre, Apr 06 2002

Extensions

a(0)=1 from Alois P. Heinz, Apr 01 2016

Status

approved