1,6

Checked up to 29:th row. Similar to A133232 and A133233. In this table the prime powers with the same base are in the same column. A prime power occurs in the table: (base of prime power-1)*(the prime power).

T(n,k) = if k=1 then 1 elseif n-1>=(A089026(n-1))^0 and n-1<(A089026(n-1))^1 then (A089026(n-1))^0 elseif n-1>=(A089026(n-1))^1 and n-1<(A089026(n-1))^2 then (A089026(n-1))^1 elseif n-1>=(A089026(n-1))^2 and n-1<(A089026(n-1))^3 then (A089026(n-1))^2 elseif n-1>=(A089026(n-1))^3 and n-1<(A089026(n-1))^4 then (A089026(n-1))^3 elseif n-1>=(A089026(n-1))^4 and n-1<(A089026(n-1))^5 then (A089026(n-1))^4 else 1 (1<=k<=n) And so on, this formula needs to be expanded if one wants to make a bigger table. A089026(n-1) means that the index to the that sequence is shifted in this formula so that the first term in A089026 is used in the second column of the table.

lcm{1}= 1

lcm{1,1} = 1

lcm{1,1,2} = 2

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

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

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

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

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

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

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

1 = 1

1*1 = 1

1*1*2 = 2

1*1*2*3 = 6

1*1*4*3*1 = 12

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

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

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

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

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

(Excel cell formula) =if(column()=1; 1; if(and(row()-1>=(A089026(n-1))^0; row()-1<(A089026(n-1))^1); (A089026(n-1))^0; if(and(row()-1>=(A089026(n-1))^1; row()-1<(A089026(n-1))^2); (A089026(n-1))^1; if(and(row()-1>=(A089026(n-1))^2; row()-1<(A089026(n-1))^3); (A089026(n-1))^2; if(and(row()-1>=(A089026(n-1))^3; row()-1<(A089026(n-1))^4); (A089026(n-1))^3; if(and(row()-1>=(A089026(n-1))^4; row()-1<(A089026(n-1))^5); (A089026(n-1))^4; 1)))))) And so on.

Cf. A089026, A003418, A000961.

Sequence in context: A096921 A037161 A156041 this_sequence A145972 A152650 A161789

Adjacent sequences: A133252 A133253 A133254 this_sequence A133256 A133257 A133258

nonn,tabl,uned

Mats Granvik (mgranvik(AT)abo.fi), Oct 14 2007