A056670 Largest non-unitary prime factor of A001405(n) = binomial(n, floor(n/2)), or 1 if no such prime exists.

1, 1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 2, 2, 2, 3, 3, 1, 2, 1, 2, 2, 2, 1, 2, 5, 5, 5, 5, 3, 3, 3, 3, 3, 3, 5, 5, 5, 5, 3, 3, 2, 2, 2, 2, 5, 5, 5, 5, 7, 7, 7, 7, 7, 7, 2, 2, 2, 2, 2, 2, 2, 2, 7, 7, 7, 7, 7, 7, 3, 3, 1, 2, 2, 2, 5, 5, 7, 7, 7, 7, 7, 7, 3, 3, 5, 5, 5, 5, 3, 3, 7, 7, 7, 7, 7, 7, 5, 5, 3, 3, 3, 3, 3, 3, 3

Offset: 1

Author

Labos Elemer, Aug 10 2000

Keywords

• nonn

Comments

The largest prime divisor of A056057(n), the largest square divisor of binomial(n, floor(n/2)), or 1 if no such prime exists.

Examples

			For n = 28: binomial(28,14) = 2*2*2*3*3*3*5*5*17*19*23, so a(28) = 5.
For n = 342: binomial(342,171) = 32*F, where F is squarefree, so a(341) = 2.
		

Links

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

Crossrefs

Cf. A001405, A006530, A056057, A056175.

Programs

Mathematica

a[n_] := Module[{f = Select[FactorInteger[Binomial[n, Floor[n/2]]], Last[#] > 1 &]}, If[f == {}, 1, f[[-1, 1]]]]; Array[a, 100] (* Amiram Eldar, Oct 05 2024 *)

Formula

a(n) = A006530(A056057(n)).