A048633 Largest squarefree number dividing n-th central binomial coefficient C(n,[ n/2 ]).

1, 2, 3, 6, 10, 10, 35, 70, 42, 42, 462, 462, 858, 858, 2145, 4290, 24310, 24310, 92378, 92378, 176358, 176358, 1352078, 1352078, 520030, 520030, 222870, 222870, 6463230, 6463230, 100180065, 200360130, 129644790, 129644790, 907513530

Offset

1,2

Comments

a(2k+1)=a(2k+2) unless 2k+1 is in A000225, in which case a(2k+2)=2*a(2k+1). - Robert Israel, Jan 21 2020

Links

Robert Israel, Table of n, a(n) for n = 1..3364

Example

n=10: C(10,5)=252=2*2*3*3*7. The largest squarefree number dividing the 10th central binomial coefficient is 2*3*7=42. Thus a(10)=42

Maple

f:= n -> convert(numtheory:-factorset(binomial(n, floor(n/2))), `*`):
map(f, [$1..50]); # Robert Israel, Jan 21 2020

Mathematica

Table[Last@ Select[Divisors@ Binomial[n, Floor[n/2]], SquareFreeQ], {n, 35}] (* Michael De Vlieger, Feb 05 2017 *)

Prog

(PARI) a(n)=factorback(factor(binomial(n, n\2))[, 1]) \\ Charles R Greathouse IV, Nov 05 2017
(Magma) [&*PrimeDivisors(Binomial(n, Floor(n/2))): n in [1..35]]; // Marius A. Burtea, Jan 21 2020

Crossrefs

Equals A007947(A001405(n)). Cf. A034973, A000225.

See A056058 for another version.

Sequence in context: A352722 A028255 A342766 * A225175 A286954 A047402

Adjacent sequences: A048630 A048631 A048632 * A048634 A048635 A048636

Keyword

nonn

Author

Labos Elemer

Status

approved