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A144379
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Triangle read by rows, first n terms of an array formed by A054521 * A054521(transform).
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2
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1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 2, 2, 4, 1, 1, 1, 1, 1, 2, 1, 1, 2, 2, 4, 2, 6, 1, 1, 1, 2, 2, 2, 3, 4, 1, 1, 2, 1, 3, 2, 4, 3, 6, 1, 1, 1, 2, 2, 1, 2, 3, 2, 4, 1, 1, 2, 2, 4, 2, 6, 4, 6, 4, 10, 1, 1, 1, 1, 1, 2, 2, 3, 3, 2, 3, 4, 1, 1, 2, 2, 4, 2, 6, 4, 6, 4, 10, 4, 12, 1, 1, 1, 2, 2, 2, 3, 3, 2, 3, 4, 3, 5
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,6
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COMMENTS
| Right border = phi(n): (1, 1, 2, 2, 4, 2, 6, 4, 6, 4, 10,...).
Row sums = A125728: (1, 2, 4, 5, 10, 7, 18, 16, 23,...) = the number of positive integers less <=k coprime to both k and n.
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FORMULA
| Given A054521 as an infinite lower triangular matrix, perform A054521(transform). Multiply the result by A054521 getting an array, then extract the first n terms of each row to form a new triangle.
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EXAMPLE
| A054521 * A054521(transform) =
1, 1, 1, 1, 1, 1, 1,...
1, 1, 1, 1, 1, 1, 1,...
1, 1, 2, 1, 2, 1, 2,...
1, 1, 1, 2, 2, 1, 2,...
1, 1, 2, 2, 4, 1, 4,...
...
Then extract the lower half of the array including the diagonal, A000010, phi(n); getting triangle A144379:
1;
1, 1;
1, 1, 2
1, 1, 1, 2;
1, 1, 2, 2, 4;
1, 1, 1, 1, 1, 2;
1, 1, 2, 2, 4, 2, 6;
1, 1, 1, 2, 2, 2, 3, 4;
1, 1, 2, 1, 3, 2, 4, 3, 6;
1, 1, 1, 2, 2, 1, 2, 3, 2, 4;
1, 1, 2, 2, 4, 2, 6, 4, 6, 4, 10;
...
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CROSSREFS
| A054521, Cf. A000010, A125728
Sequence in context: A029444 A122191 A097847 * A107435 A196056 A161095
Adjacent sequences: A144376 A144377 A144378 * A144380 A144381 A144382
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KEYWORD
| nonn,tabl
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AUTHOR
| Gary W. Adamson (qntmpkt(AT)yahoo.com), Sep 19 2008
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