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A130212
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T(k, n) = sum_(1 <= j <= k) [j | k] j mu(k / j) floor(n / k), triangle read by rows.
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4
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1, 2, 1, 3, 1, 2, 4, 2, 2, 2, 5, 2, 2, 2, 4, 5, 3, 4, 2, 4, 2, 7, 3, 4, 2, 4, 2, 6, 8, 4, 4, 4, 4, 2, 6, 4, 9, 4, 6, 4, 4, 2, 6, 4, 6, 10, 5, 6, 4, 8, 2, 6, 4, 6, 4
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Row sums = the triangular series, A000217: (1, 3, 6, 10, 15,...). Right border = A000010, phi(n): (1, 1, 2, 2, 4, 2, 6,...). A130211 = A054522 * A000012
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FORMULA
| A000012 * A054522 as infinite lower triangular matrices.
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EXAMPLE
| First few rows of the triangle are:
1;
2, 1;
3, 1, 2;
4, 2, 2, 2;
5, 2, 2, 2, 4;
6, 3, 4, 2, 4, 2;
7, 3, 4, 2, 4, 2, 6;
8, 4, 4, 4, 4, 2, 6, 4;
9, 4, 6, 4, 4, 2, 6, 4, 6;
10, 5, 6, 4, 8, 2, 6, 4, 6, 4;
...
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CROSSREFS
| with(numtheory): A130212 := (n, k) -> add(j*mobius(k / j)*iquo(n, k), j = divisors(k)); [From Peter Luschny (peter(AT)luschny.de), Oct 28 2010]
Cf. A000010, A130211, A054522, A000217.
Sequence in context: A175344 A130517 A056951 * A133737 A125047 A045898
Adjacent sequences: A130209 A130210 A130211 * A130213 A130214 A130215
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KEYWORD
| nonn,tabl
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AUTHOR
| Gary W. Adamson (qntmpkt(AT)yahoo.com), May 17 2007
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EXTENSIONS
| Name (was: A000012*A054522) replaced by new formula. - Peter Luschny (peter(AT)luschny.de), Oct 28 2010
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