cp's OEIS Frontend

A055230 Greatest common divisor of largest square dividing n! and squarefree part of n!.

%I A055230 #19 Aug 13 2024 21:01:33
%S A055230 1,1,1,2,2,1,1,2,2,1,1,3,3,6,10,10,10,5,5,1,21,42,42,7,7,14,42,6,6,5,
%T A055230 5,10,330,165,231,231,231,462,2002,5005,5005,4290,4290,390,78,39,39,
%U A055230 13,13,26,1326,102,102,17,935,13090,746130,373065,373065,24871,24871
%N A055230 Greatest common divisor of largest square dividing n! and squarefree part of n!.
%H A055230 Michael De Vlieger, <a href="/A055230/b055230.txt">Table of n, a(n) for n = 1..5000</a>
%F A055230 a(n) = GCD(A008833(n!), A007913(n!)) = GCD(A055071(n), A055204(n)).
%e A055230 a(5) = 2 because 5! = 120; largest square divisor is 4, squarefree part is 30; GCD(4, 30) = 2.
%e A055230 a(7) = 1 because 7! = 5040; the largest square divisor is 144 and the squarefree part is 35 and these are coprime.
%t A055230 Table[GCD[Times @@ Flatten@ Map[Table[#1, 2 Floor[#2/2]] & @@ # &, #], Times @@ Flatten@ Map[Table[#1, Floor[Mod[#2, 2]]] & @@ # &, #]] &@ FactorInteger[n!], {n, 61}] (* _Michael De Vlieger_, Jul 26 2016 *)
%o A055230 (PARI) a(n) = my(fn=n!, cn=core(fn)); gcd(cn, fn/cn); \\ _Michel Marcus_, Dec 10 2013
%Y A055230 Cf. A008833, A007913, A000188, A000720.
%K A055230 nonn
%O A055230 1,4
%A A055230 _Labos Elemer_, Jun 21 2000