A133233 Triangle A133232 read by rows with an additional column T(n,0)=1 added to the left.

1, 1, 1, 1, 1, 2, 1, 1, 2, 3, 1, 1, 1, 3, 4, 1, 1, 1, 3, 4, 5, 1, 1, 1, 3, 4, 5, 1, 1, 1, 1, 3, 4, 5, 1, 7, 1, 1, 1, 3, 1, 5, 1, 7, 8, 1, 1, 1, 1, 1, 5, 1, 7, 8, 9, 1, 1, 1, 1, 1, 5, 1, 7, 8, 9, 1, 1, 1, 1, 1, 1, 5, 1, 7, 8, 9, 1, 11, 1, 1, 1, 1, 1, 5, 1, 7, 8, 9, 1, 11, 1, 1, 1, 1, 1, 1, 5, 1, 7, 8, 9, 1, 11

Offset: 0

Author

Mats Granvik, Oct 13 2007

Keywords

• nonn
• tabl

Comments

Attaching an additional 1 does not change the composition compared to A133232 since neither the LCM over the elements of a row nor their product is affected.

Examples

			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
		

Links

• Mats Granvik, Table of n, a(n) for n = 0..434

Crossrefs

Cf. A003418, A120112, A000961, A014963.

Formula

T(n,0) = 1.

T(n,k) = A133232(n,k), k>0.

Extensions

Removed information which duplicates A133232; offset set to 0 - R. J. Mathar, Nov 23 2010