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

0,6

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.

Links

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

Formula

T(n,0) = 1.

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

Example

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

Crossrefs

Cf. A003418, A120112, A000961, A014963.

Sequence in context: A161161 A350357 A136277 * A174430 A116361 A375571

Adjacent sequences: A133230 A133231 A133232 * A133234 A133235 A133236

Keyword

nonn,tabl

Author

Mats Granvik, Oct 13 2007

Extensions

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

Status

approved