A055071 Largest square dividing n!.

1, 1, 1, 4, 4, 144, 144, 576, 5184, 518400, 518400, 2073600, 2073600, 101606400, 914457600, 14631321600, 14631321600, 526727577600, 526727577600, 52672757760000, 52672757760000, 6373403688960000, 6373403688960000

Offset

1,4

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..500

Formula

a(n)=A008833(n!).

log a(n) ~ n log n. - Charles R Greathouse IV, Apr 04 2012

Maple

seq(expand(numtheory[nthpow](n!, 2)), n=1..26); # Peter Luschny, Apr 03 2013

Mathematica

a[n_] := Select[Reverse @ Divisors[n!], IntegerQ[Sqrt[#]] &, 1] // First; a /@ Range[23] (* Jean-François Alcover, May 19 2011 *)

Prog

(PARI) a(n)=core(n!, 2)[2]^2 \\ Charles R Greathouse IV, Apr 04 2012

Crossrefs

Cf. A000188, A008833.

Sequence in context: A163196 A219453 A283453 * A213142 A357540 A097572

Adjacent sequences: A055068 A055069 A055070 * A055072 A055073 A055074

Keyword

nonn

Author

Labos Elemer, Jun 13 2000

Extensions

More terms from James A. Sellers, Jun 20 2000

Status

approved