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A055772 Square root of largest square dividing n!. 16
1, 1, 1, 2, 2, 12, 12, 24, 72, 720, 720, 1440, 1440, 10080, 30240, 120960, 120960, 725760, 725760, 7257600, 7257600, 79833600, 79833600, 958003200, 4790016000, 62270208000, 186810624000, 2615348736000, 2615348736000, 15692092416000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

LINKS

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

FORMULA

a(n) = A000188(n!) = sqrt(A008833(n!)) = sqrt(A055071(n)).

n! = a(n)^2*A055204(n) = a(n)^2*A007913(n!).

n! = (A000188(n!)^2)*A055229(n!)*A055231(n!).

log(a(n)) ~ n*log(n)/2. - David Radcliffe, Oct 17 2014

EXAMPLE

For n=6, 6!=720=144*5 so a(6)=sqrt(144)=12.

MAPLE

a:= proc(n)

local r, F, t;

r:= n!;

F:= ifactors(r)[2];

mul(t[1]^floor(t[2]/2), t=F)

end proc:

seq(a(n), n= 1 .. 100); # Robert Israel, Oct 19 2014

MATHEMATICA

Table[Last[Select[Sqrt[#]&/@Divisors[n!], IntegerQ]], {n, 30}] (* Harvey P. Dale, Oct 08 2012 *)

(Sqrt@Factorial@Range@30)/.Sqrt[_]->1 (* Morgan L. Owens, May 04 2016 *)

PROG

(PARI) a(n)=core(n!, 2)[2] \\ Charles R Greathouse IV, Apr 03 2012

CROSSREFS

Cf. A000188, A008833, A007913, A055229, A055231, A055071, A055204, A055230.

Sequence in context: A131121 A232853 A328520 * A025527 A205957 A092144

Adjacent sequences:  A055769 A055770 A055771 * A055773 A055774 A055775

KEYWORD

nonn

AUTHOR

Labos Elemer, Jul 12 2000

STATUS

approved

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Last modified January 19 04:09 EST 2020. Contains 331031 sequences. (Running on oeis4.)