A133255 - OEIS

A133255

Triangle with a minimum occurrence of prime powers for which the least common multiple of the rows will give the terms in A003418.

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

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OFFSET

1,6

COMMENTS

Checked up to 29th 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).

LINKS

Table of n, a(n) for n=1..104.

FORMULA

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 that sequence is shifted in this formula so that the first term in A089026 is used in the second column of the table.

EXAMPLE

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

PROG

(Excel) =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.

CROSSREFS

Cf. A089026, A003418, A000961.

Sequence in context: A168443 A156041 A306210 * A354273 A282748 A145972

Adjacent sequences: A133252 A133253 A133254 * A133256 A133257 A133258

KEYWORD

nonn,tabl,uned

AUTHOR

Mats Granvik, Oct 14 2007

STATUS

approved