A093432 a(n) = lcm_{k=1..n} (lcm(n,n-1,...,n-k+2,n-k+1)/lcm(1,2,...,k)).

1, 2, 3, 12, 10, 30, 105, 280, 252, 1260, 2310, 4620, 4290, 6006, 15015, 240240, 680680, 6126120, 11639628, 2771340, 1763580, 19399380, 223092870, 178474296, 171609900, 743642900, 1434168450, 20078358300, 19409079690, 19409079690, 300840735195, 875173047840

Offset: 1

Author

Amarnath Murthy, Mar 31 2004

Keywords

• nonn

Examples

			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.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..2363

Crossrefs

Cf. A093430, A093431, A093433.

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

Programs

Maple

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
# second Maple program:
b:= proc(n) option remember; `if`(n=1, 1, ilcm(b(n-1), n)) end:
a:= proc(n) option remember; local k, r, s; r, s:= 1, 1;
      for k to n do s:= ilcm(s,n-k+1); r:= ilcm(r,s/b(k)) od; r
    end:
seq(a(n), n=1..40);  # Alois P. Heinz, Mar 17 2018

Mathematica

b[n_] := b[n] = If[n == 1, 1, LCM[b[n - 1], n]];
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];
Array[a, 40] (* Jean-François Alcover, Jun 18 2018, after Alois P. Heinz *)

Extensions

Corrected and extended by Emeric Deutsch, Jan 30 2006