1,6

Checked up to 29:th row. A column that is a prime ends at row = p^2 (and continues with ones) while a column that is a prime power ends at row = its base times the prime power. The ones are there for the least common multiple to calculate correctly.

Mats Granvik (mgranvik(AT)abo.fi), Oct 13 2007, Table of n, a(n) for n = 1..435

T(n,k) = if n>=k+k*abs(A120112) then k else 1 (1<=k<=n) (Not exactly though, this formula generates the table from the second column onwards.)

T(n,k) = if n < A014963*A100994 then A100994 else 1 (1<=k<=n) (likewise, from the second column onwards). - Mats Granvik (mgranvik(AT)abo.fi), Jan 21 2008

1 will occur 1*1 = 1 times

2 will occur 2*1 = 2 times

3 will occur 3*2 = 6 times

4 will occur 4*1 = 4 times

5 will occur 5*4 = 20 times

The first rows of the triangle and the least common multiple of the rows are:

lcm{1} = 1

lcm{1, 1} = 1

lcm{1, 1, 2} = 2

lcm{1, 1, 2, 3} = 6

lcm{1, 1, 1, 3, 4} = 12

lcm{1, 1, 1, 3, 4, 5} = 60

lcm{1, 1, 1, 3, 4, 5, 1} = 60

lcm{1, 1, 1, 3, 4, 5, 1, 7} = 420

lcm{1, 1, 1, 3, 1, 5, 1, 7, 8} = 840

lcm{1, 1, 1, 1, 1, 5, 1, 7, 8, 9} = 2520

Multiplying the terms in the rows produces the same result:

1 = 1

1*1 = 1

1*1*2 = 2

1*1*2*3 = 6

1*1*1*3*4 = 12

1*1*1*3*4*5 = 60

1*1*1*3*4*5*1 = 60

1*1*1*3*4*5*1*7 = 420

1*1*1*3*1*5*1*7*8 = 840

1*1*1*1*1*5*1*7*8*9 = 2520

(Excel cell formula) =if(and(row()>=column(); row()<column()+column()*abs(A120112)); column(); 1) (Generates the table from the second column onwards)

(Excel cell formula) =if(and(n>=k; n<A014963*A100994); A100994; 1) - Mats Granvik (mgranvik(AT)abo.fi), Jan 21 2008

Cf. A003418, A120112, A000961.

Cf. A014963.

Sequence in context: A126387 A038374 A136277 this_sequence A116361 A106796 A082850

Adjacent sequences: A133230 A133231 A133232 this_sequence A133234 A133235 A133236

nonn,tabl,uned

Mats Granvik (mgranvik(AT)abo.fi), Oct 13 2007