|
|
A133233
|
|
Triangle A133232 read by rows with an additional column T(n,0)=1 added to the left.
|
|
9
|
|
|
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
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
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
|
|
|
FORMULA
|
T(n,0) = 1.
|
|
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
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|