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

1,4

Links

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

Formula

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

Example

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.

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 *)

Prog

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

Crossrefs

Cf. A008833, A007913, A000188, A000720.

Sequence in context: A293773 A071017 A112049 * A290262 A112050 A283156

Adjacent sequences: A055227 A055228 A055229 * A055231 A055232 A055233

Keyword

nonn

Author

Labos Elemer, Jun 21 2000

Status

approved