login
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.
3
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.
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
KEYWORD
nonn,tabl
AUTHOR
Amarnath Murthy, Apr 29 2004
EXTENSIONS
More terms from R. J. Mathar, Apr 30 2007
STATUS
approved