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Search: id:A133232
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| A133232 |
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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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6
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| 1, 1, 2, 1, 2, 3, 1, 1, 3, 4, 1, 1, 3, 4, 5, 1, 1, 3, 4, 5, 1, 1, 1, 3, 4, 5, 1, 7, 1, 1, 3, 1, 5, 1, 7, 8, 1, 1, 1, 1, 5, 1, 7, 8, 9, 1, 1, 1, 1, 5, 1, 7, 8, 9, 1, 1, 1, 1, 1, 5, 1, 7, 8, 9, 1, 11, 1, 1, 1, 1, 5, 1, 7, 8, 9, 1, 11, 1, 1, 1, 1, 1, 5, 1, 7, 8, 9, 1, 11, 1, 13, 1, 1, 1, 1, 5, 1, 7, 8, 9, 1, 11, 1
(list; table; graph; listen)
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OFFSET
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1,3
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COMMENT
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Checked up to 28:th row. The rest of the ones in the table are there for the least common multiple to calculate correctly.
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LINKS
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Mats Granvik (mgranvik(AT)abo.fi), Oct 13 2007, Table of n, a(n) for n = 1..406
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FORMULA
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T(n,k) = if n<k+k*abs(A120112) then k else 1 (1<=k<=n)
T(n,k) = if n<A014963*A100994 then A100994 else 1 (1<=k<=n) - Mats Granvik (mgranvik(AT)abo.fi), Jan 21 2008
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EXAMPLE
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1 will occur 1*1 = 1 times in column 1
2 will occur 2*1 = 2 times in column 2
3 will occur 3*2 = 6 times in column 3
4 will occur 4*1 = 4 times in column 4
5 will occur 5*4 = 20 times in column 5
The first rows of the triangle and the least common multiple of the rows are:
lcm{1} = 1
lcm{1, 2} = 2
lcm{1, 2, 3} = 6
lcm{1, 1, 3, 4} = 12
lcm{1, 1, 3, 4, 5} = 60
lcm{1, 1, 3, 4, 5, 1} = 60
lcm{1, 1, 3, 4, 5, 1, 7} = 420
lcm{1, 1, 3, 1, 5, 1, 7, 8} = 840
lcm{1, 1, 1, 1, 5, 1, 7, 8, 9} = 2520
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PROGRAM
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(Excel cell formula) =if(and(row()>=column(); row()<column()+column()*abs(A120112)); column(); 1)
(Excel cell formula) =if(and(n>=k; n<A014963*A100994); A100994; 1) - Mats Granvik (mgranvik(AT)abo.fi), Jan 21 2008
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CROSSREFS
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Cf. A003418, A120112.
Cf. A014963.
Sequence in context: A131794 A133674 A098666 this_sequence A137152 A109004 A103823
Adjacent sequences: A133229 A133230 A133231 this_sequence A133233 A133234 A133235
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KEYWORD
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nonn,tabl,uned
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AUTHOR
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Mats Granvik (mgranvik(AT)abo.fi), Oct 13 2007
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