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A127481
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Triangle T(n,k) read by rows: T(n,k) = sum_{l=k..n, l|n, k|l} l*phi(k).
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1
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1, 3, 2, 4, 0, 6, 7, 6, 0, 8, 6, 0, 0, 0, 20, 12, 8, 18, 0, 0, 12, 8, 0, 0, 0, 0, 0, 42, 15, 14, 0, 24, 0, 0, 0, 32, 13, 0, 24, 0, 0, 0, 0, 0, 54, 18, 12, 0, 0, 60, 0, 0, 0, 0, 40, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 110, 28, 24, 42, 32, 0, 36, 0, 0, 0, 0, 0, 48, 14, 0, 0, 0, 0, 0, 0, 0, 0
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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FORMULA
| T(n,1) = A000203(n).
T(n,n) = A002618(n).
T(n,k) =sum_{l=k..n} A127093(n,l) * A054522(l,k), the matrix product of the infinite lower triangular matrices.
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EXAMPLE
| First few rows of the triangle are:
1;
3, 2;
4, 0, 6;
7, 6, 0, 8;
6, 0, 0, 0, 20,
12, 8, 18, 0, 0, 12;
8, 0, 0, 0, 0, 0, 42;
15, 14, 0, 24, 0, 0, 0, 32;
...
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CROSSREFS
| Cf. A054522, A127093, A001157 (row sums), A002618, A127466.
Sequence in context: A129237 A127099 A004545 * A154879 A097673 A140430
Adjacent sequences: A127478 A127479 A127480 * A127482 A127483 A127484
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KEYWORD
| nonn,tabl,easy
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AUTHOR
| Gary W. Adamson (qntmpkt(AT)yahoo.com), Jan 15 2007
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