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

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, 5, 10, 330, 165, 231, 231, 231, 462, 2002, 5005, 5005, 4290, 4290, 390, 78, 39, 39, 13, 13, 26, 1326, 102, 102, 17, 935, 13090, 746130, 373065, 373065, 24871, 24871

Offset: 1

Author

Labos Elemer, Jun 21 2000

Keywords

• nonn

Examples

			a(5) = 2 because 5! = 120; largest square divisor is 4, squarefree part is 30; GCD(4, 30) = 2.
a(7) = 1 because 7! = 5040; the largest square divisor is 144 and the squarefree part is 35 and these are coprime.
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..5000

Crossrefs

Cf. A008833, A007913, A000188, A000720.

Programs

Mathematica

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 *)

PARI

a(n) = my(fn=n!, cn=core(fn)); gcd(cn, fn/cn); \\ Michel Marcus, Dec 10 2013

Formula

a(n) = GCD(A008833(n!), A007913(n!)) = GCD(A055071(n), A055204(n)).