A198481 Square root of the largest square dividing ((2n-1)!)^(2n-3).

1, 1, 240, 304819200, 3440500260470784000, 1827912356210202139164672000000000, 13482302715547740229948201750717130814259200000000000

Offset: 1

Author

Artur Jasinski, Oct 25 2011

Keywords

• nonn

Comments

For the complementary squarefree parts see A197880.

Crossrefs

Cf. A134367, A197880.

Programs

Maple

A000188 := proc(n)
        a := 1 ;
        for pf in ifactors(n)[2] do
                p := op(1,pf) ;
                e := op(2,pf) ;
                a := a*p^(floor(e/2)) ;
        end do:
        a ;
end proc:
A198481 := proc(n)
        A000188( A134367(2*n-1)) ;
end proc:
seq(A198481(n),n=1..10) ; # R. J. Mathar, Oct 25 2011

Mathematica

aa = {}; data = Table[kk = Sqrt[(n!)^(n - 2)], {n, 1, 100, 2}]; sp = data /. Sqrt[_] -> 1; sfp = data/sp; sp
Sqrt[#]&/@Table[Max[Select[Divisors[((2n-1)!)^(2n-3)],IntegerQ[Sqrt[#]]&]],{n,7}] (* Harvey P. Dale, May 24 2024 *)

Formula

a(n) = A000188(A134367(2*n-1)). - R. J. Mathar, Oct 25 2011