OFFSET
1,3
COMMENTS
Checked up to 28th row. The rest of the ones in the table are there for the least common multiple to calculate correctly.
LINKS
Mats Granvik, Oct 13 2007, Table of n, a(n) for n = 1..406
FORMULA
T(n,k) = if n<k+k*|A120112(k-1)| then k, else 1 (1<=k<=n).
T(n,k) = if n < A014963(k)*A100994(k) then A100994(k), else 1 (1<=k<=n). - Mats Granvik, Jan 21 2008
EXAMPLE
2 occurs 2*1 = 2 times in column 2.
3 occurs 3*2 = 6 times in column 3.
4 occurs 4*1 = 4 times in column 4.
5 occurs 5*4 = 20 times in column 5.
k occurs A133936(k) times in column k. The first rows of the triangle and the least common multiple of the rows are:
lcm{1} = 1
lcm{1, 2} = 2
lcm{1, 2, 3} = 6
lcm{1, 1, 3, 4} = 12
lcm{1, 1, 3, 4, 5} = 60
lcm{1, 1, 3, 4, 5, 1} = 60
lcm{1, 1, 3, 4, 5, 1, 7} = 420
lcm{1, 1, 3, 1, 5, 1, 7, 8} = 840
lcm{1, 1, 1, 1, 5, 1, 7, 8, 9} = 2520
MAPLE
A120112 := proc(n) 1-ilcm(seq(i, i=1..n+1))/ilcm(seq(i, i=1..n)) ; end proc:
seq(seq(A133232(n, k), k=1..n), n=1..15) ; # R. J. Mathar, Nov 23 2010
MATHEMATICA
b[n_] := b[n] = If[n == 0, 1, LCM @@ Range[n]];
c[n_] := 1 - b[n+1]/b[n];
T[n_, k_] := If[n < k*(1+Abs[c[k-1]]), k, 1];
Table[T[n, k], {n, 1, 10}, {k, 1, n}] // Flatten (* Jean-François Alcover, Mar 01 2021 *)
PROG
(Excel) =if(and(row()>=column(); row()<column()+column()*abs(A120112)); column(); 1)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Mats Granvik, Oct 13 2007
EXTENSIONS
Indices added to formulas by R. J. Mathar, Nov 23 2010
STATUS
approved