A133233 - OEIS

%I #18 Jan 01 2018 04:13:11

%S 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,

%T 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,

%U 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

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

%C 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.

%H Mats Granvik, <a href="/A133233/b133233.txt">Table of n, a(n) for n = 0..434</a>

%F T(n,0) = 1.

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

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

%e lcm{1} = 1

%e lcm{1, 1} = 1

%e lcm{1, 1, 2} = 2

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

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

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

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

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

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

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

%e Multiplying the terms in the rows produces the same result:

%e 1 = 1

%e 1*1 = 1

%e 1*1*2 = 2

%e 1*1*2*3 = 6

%e 1*1*1*3*4 = 12

%e 1*1*1*3*4*5 = 60

%e 1*1*1*3*4*5*1 = 60

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

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

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

%Y Cf. A003418, A120112, A000961, A014963.

%K nonn,tabl

%O 0,6

%A _Mats Granvik_, Oct 13 2007

%E Removed information which duplicates A133232; offset set to 0 - _R. J. Mathar_, Nov 23 2010