A093432 - OEIS

%I #13 Jun 18 2018 10:54:36

%S 1,2,3,12,10,30,105,280,252,1260,2310,4620,4290,6006,15015,240240,

%T 680680,6126120,11639628,2771340,1763580,19399380,223092870,178474296,

%U 171609900,743642900,1434168450,20078358300,19409079690,19409079690,300840735195,875173047840

%N a(n) = lcm_{k=1..n} (lcm(n,n-1,...,n-k+2,n-k+1)/lcm(1,2,...,k)).

%H Alois P. Heinz, <a href="/A093432/b093432.txt">Table of n, a(n) for n = 1..2363</a>

%e a(4) = lcm(lcm(4)/lcm(1), lcm(4,3)/lcm(1,2), lcm(4,3,2)/lcm(1,2,3), lcm(4,3,2,1)/lcm(1,2,3,4)) = lcm(4,6,2,1) = 12.

%p T:=(n,k)->lcm(seq(i,i=n-k+1..n))/lcm(seq(j,j=1..k)): seq(lcm(seq(T(n,k),k=1..n)),n=1..35); # _Emeric Deutsch_, Jan 30 2006

%p # second Maple program:

%p b:= proc(n) option remember; `if`(n=1, 1, ilcm(b(n-1), n)) end:

%p a:= proc(n) option remember; local k, r, s; r, s:= 1, 1;

%p       for k to n do s:= ilcm(s,n-k+1); r:= ilcm(r,s/b(k)) od; r

%p     end:

%p seq(a(n), n=1..40);  # _Alois P. Heinz_, Mar 17 2018

%t b[n_] := b[n] = If[n == 1, 1, LCM[b[n - 1], n]];

%t a[n_] := a[n] = Module[{k, r = 1, s = 1}, For[k = 1, k <= n, k++, s = LCM[s, n - k + 1]; r = LCM[r, s/b[k]]]; r];

%t Array[a, 40] (* _Jean-François Alcover_, Jun 18 2018, after _Alois P. Heinz_ *)

%Y Cf. A093430, A093431, A093433.

%Y LCM of the terms in row n of the triangle in A093430.

%K nonn

%O 1,2

%A _Amarnath Murthy_, Mar 31 2004

%E Corrected and extended by _Emeric Deutsch_, Jan 30 2006