A094307 The k-th term of the n-th row of the following triangle is the least common multiple of all numbers from 1 to n except k. Sequence contains the triangle by rows.

1, 2, 1, 6, 3, 2, 12, 12, 4, 6, 60, 60, 20, 30, 12, 60, 60, 60, 30, 12, 60, 420, 420, 420, 210, 84, 420, 60, 840, 840, 840, 840, 168, 840, 120, 420, 2520, 2520, 2520, 2520, 504, 2520, 360, 1260, 840, 2520, 2520, 2520, 2520, 2520, 2520, 360, 1260, 840, 2520, 27720

Offset

1,2

Comments

The leading diagonal and the first column are given by A003418 with a suitable offset 0 or 1.

Links

Table of n, a(n) for n=1..56.

Formula

T(n,k) = A003418(n)/p if k = p^m for some m and n < 2*p^m and A003418(n) otherwise. - Charlie Neder, Jun 13 2019

Example

Triangle begins:
   1,
   2,  1,
   6,  3,  2,
  12, 12,  4,  6,
  60, 60, 20, 30, 12,
  60, 60, 60, 30, 12, 60;

Maple

A094307 := proc(n, k) local a, i ; if n = 1 then RETURN(1) ; elif k > 1 and k < n then a := [seq(i, i=1..k-1), seq(i, i=k+1..n)] ; elif k = n then a := [seq(i, i=1..k-1)] ; else a := [seq(i, i=2..n)] ; fi ; ilcm(op(a)) ; end: for n from 1 to 15 do for k from 1 to n do printf("%d, ", A094307(n, k)) ; od ; od ; # R. J. Mathar, Apr 30 2007

Mathematica

T[n_, k_] := LCM @@ Which[n == 1, {1}, 1 < k < n, Join[Range[k-1], Range[k+1, n]], k == n, Range[k-1], True, Range[2, n]];
Table[T[n, k], {n, 1, 15}, {k, 1, n}] // Flatten (* Jean-François Alcover, May 20 2020 *)

Prog

(PARI) T(n, k) = lcm(setminus(vector(n, i, i), Set(k)));
tabl(nn) = {for (n=1, nn, for (k=1, n, print1(T(n, k), ", "); ); print(); ); } \\ Michel Marcus, Jun 15 2019

Crossrefs

Cf. A094308.

Sequence in context: A252095 A120435 A125901 * A097905 A094310 A165908

Adjacent sequences: A094304 A094305 A094306 * A094308 A094309 A094310

Keyword

nonn,tabl

Author

Amarnath Murthy, Apr 29 2004

Extensions

More terms from R. J. Mathar, Apr 30 2007

Status

approved