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A133255
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Triangle with a minimum occurrence of prime powers for which the least common multiple of the rows will give the terms in A003418.
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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
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,6
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COMMENTS
| 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).
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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 the that sequence is shifted in this formula so that the first term in A089026 is used in the second column of the table.
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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
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PROG
| (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.
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CROSSREFS
| Cf. A089026, A003418, A000961.
Sequence in context: A202176 A168443 A156041 * A145972 A152650 A184219
Adjacent sequences: A133252 A133253 A133254 * A133256 A133257 A133258
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KEYWORD
| nonn,tabl,uned
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AUTHOR
| Mats Granvik (mgranvik(AT)abo.fi), Oct 14 2007
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