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A127569
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Triangle read by rows: product of the Mobius matrix A054525 by the diagonal matrix diag(A000230(n)).
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2
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1, -1, 3, -1, 0, 4, 0, -3, 0, 7, -1, 0, 0, 0, 6, 1, -3, -4, 0, 0, 12, -1, 0, 0, 0, 0, 0, 8, 0, 0, 0, -7, 0, 0, 0, 15, 0, 0, -4, 0, 0, 0, 0, 0, 13, 1, -3, 0, 0, -6, 0, 0, 0, 0, 18, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 3, 0, -7, 0, -12, 0, 0, 0, 0, 0, 28, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14, 1, -3, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 24, 1, 0, -4, 0, -6, 0, 0, 0, 0, 0
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| Left column = mu(n), A008683; right border = sigma(n), A000203; row sums = n.
The definition of Mobius transform is extended to matrices here in the sense of "left multiplication by the Mobius matrix A054525". - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 02 2007
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FORMULA
| T(n,k)=A054525(n,k)*A000203(k). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 02 2007
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EXAMPLE
| First few rows of the triangle are:
1;
-1, 3;
-1, 0, 4;
0, -3, 0, 7;
-1, 0, 0, 0, 6;
1, -3, -4, 0, 0, 12;
...
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MAPLE
| A000203T := proc(n, k) if n = k then numtheory[sigma](n) ; else 0 ; fi ; end: A054525 := proc(n, k) if n < 1 or k > n or n mod k <> 0 then 0; else numtheory[mobius](n/k) ; fi ; end: A127569 := proc(n, k) add(A054525(n, i)*A000203T(i, k), i=1..n) ; end: for n from 1 to 15 do for k from 1 to n do printf("%a, ", A127569(n, k)) ; od: od: - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 02 2007
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CROSSREFS
| Cf. A054525, A000203, A008683.
Sequence in context: A110033 A166407 A159059 * A117372 A127570 A186827
Adjacent sequences: A127566 A127567 A127568 * A127570 A127571 A127572
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KEYWORD
| tabl,sign
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AUTHOR
| Gary W. Adamson (qntmpkt(AT)yahoo.com), Jan 19 2007
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EXTENSIONS
| Missing comma corrected by Naruto Canada, Aug 26 2007
More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 02 2007
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