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A140256
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Triangle read by columns: Column k is A014963 aerated with groups of (k-1) zeros.
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7
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1, 2, 1, 3, 0, 1, 2, 2, 0, 1, 5, 0, 0, 0, 1, 1, 3, 2, 0, 0, 1, 7, 0, 0, 0, 0, 0, 1, 2, 2, 0, 2, 0, 0, 0, 1, 3, 0, 3, 0, 0, 0, 0, 0, 1, 1, 5, 0, 0, 2, 0, 0, 0, 0, 1, 11, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 3, 0, 2, 0, 0, 0, 0, 0, 1, 13, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 7, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 1
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OFFSET
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1,2
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COMMENTS
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If the row number n is prime, the row consists of T(n,1)=n followed by n-2 zeros and followed by T(n,n)=1.
Similar to A138618.
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LINKS
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Table of n, a(n) for n=1..105.
T. Tao, Simons Lecture I: Structure and randomness in Fourier analysis and number theory.
Wikipedia, Fundamental theorem of arithmetic.
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FORMULA
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T(n,k) = A014963(n/k) = A014963(A126988(n,k)) if k|n, T(n,k)=0 otherwise. 1<=k<=n.
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EXAMPLE
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First few rows of the triangle are:
1;
2, 1;
3, 0, 1;
2, 2, 0, 1;
5, 0, 0, 0, 1;
1, 3, 2, 0, 0, 1;
7, 0, 0, 0, 0, 0, 1;
2, 2, 0, 2, 0, 0, 0, 1;
3, 0, 3, 0, 0, 0, 0, 0, 1;
1, 5, 0, 0, 2, 0, 0, 0, 0, 1;
11, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1;
1, 1, 2, 3, 0, 2, 0, 0, 0, 0, 0, 1;
...
Column 2 = (1, 0, 2, 0, 3, 0, 2, 0, 5, 0, 1, 0, 7,...).
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PROG
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(Excel cell formula) =if(row()>=column(); if(mod(row(); column())=0; lookup(roundup(row()/column(); 0); A000027; A014963); 0); "")
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CROSSREFS
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Cf. A140255 (row sums), A014963.
Row products A000027. [From Mats Granvik, Oct 08 2009]
Sequence in context: A071431 A182740 A140699 * A126206 A119709 A120251
Adjacent sequences: A140253 A140254 A140255 * A140257 A140258 A140259
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KEYWORD
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nonn,tabl
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AUTHOR
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Gary W. Adamson and Mats Granvik, May 16 2008, Jun 11 2008
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STATUS
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approved
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