A366369 -id:A366369 - cp's OEIS frontend

A139550 a(n) = lcm(1..floor(n/2)).

1, 1, 1, 1, 2, 2, 6, 6, 12, 12, 60, 60, 60, 60, 420, 420, 840, 840, 2520, 2520, 2520, 2520, 27720, 27720, 27720, 27720, 360360, 360360, 360360, 360360, 360360, 360360, 720720, 720720, 12252240, 12252240, 12252240, 12252240, 232792560, 232792560

Offset: 0

Mats Granvik, Apr 27 2008

nonn

Row products of A139549.

Cf. A139549, A003418, A366368, A366369.

LCM := proc (n) local i; ilcm(seq(i,i=1..n)) end; A139550 := n -> LCM(n/2); seq(A139550(n),n=0..40); # Peter Luschny, Jun 09 2011

Join[{1,1},Table[LCM@@Range[Floor[n/2]],{n,2,40}]] (* Harvey P. Dale, Jan 12 2024 *)

a(n) = A003418(floor(n/2)) = A366368(n) / A003418(n) = A003418(n) / A366369(n). - Max Alekseyev, Oct 08 2023

Offset corrected by Peter Luschny, Jun 09 2011

A366368 a(n) = LCM of pairwise products of distinct integers from {1,2,...,n}.

Original entry on oeis.org

1, 1, 2, 6, 24, 120, 360, 2520, 10080, 30240, 151200, 1663200, 1663200, 21621600, 151351200, 151351200, 605404800, 10291881600, 30875644800, 586637251200, 586637251200, 586637251200, 6453009763200, 148419224553600, 148419224553600, 742096122768000, 9647249595984000, 28941748787952000

Offset: 0

Max Alekseyev, Oct 08 2023

nonn

A003418(n) divides a(n), which in turn divides A003418(n)^2. Furthermore, A003418(n)^2 / a(n) = A366369(n) is squarefree.

Cf. A003418, A139550, A366369.

a366368(n) = my(k,r); r=1; forprime(p=2,n, k=logint(n,p); r *= p^(2*k - (n<2*p^k)) ); r;

a(n) = A003418(n)^2 / A366369(n).

a(n) = A003418(n) * A139550(n) = A003418(n) * A003418(floor(n/2)).

cp's OEIS Frontend

A139550 a(n) = lcm(1..floor(n/2)).

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