A056670 - OEIS

%I #13 Oct 05 2024 09:08:50

%S 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,

%T 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,

%U 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

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

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

%H Amiram Eldar, <a href="/A056670/b056670.txt">Table of n, a(n) for n = 1..10000</a>

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

%e For n = 28: binomial(28,14) = 2*2*2*3*3*3*5*5*17*19*23, so a(28) = 5.

%e For n = 342: binomial(342,171) = 32*F, where F is squarefree, so a(341) = 2.

%t 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 *)

%Y Cf. A001405, A006530, A056057, A056175.

%K nonn

%O 1,6

%A _Labos Elemer_, Aug 10 2000