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A181538
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T(n, k) = sum_(1 <= j <= k) [j | k] j mu(k / j) gcd(n, k), triangle read by rows.
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3
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1, 1, 2, 1, 1, 6, 1, 2, 2, 8, 1, 1, 2, 2, 20, 1, 2, 6, 4, 4, 12, 1, 1, 2, 2, 4, 2, 42, 1, 2, 2, 8, 4, 4, 6, 32, 1, 1, 6, 2, 4, 6, 6, 4, 54, 1, 2, 2, 4, 20, 4, 6, 8, 6, 40, 1, 1, 2, 2, 4, 2, 6, 4, 6, 4, 110, 1, 2, 6, 8, 4, 12, 6, 16, 18, 8, 10, 48
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OFFSET
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1,3
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COMMENTS
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T(n,k) = gcd(n,k) phi(k). Can be seen as a generalization of n -> phi(n^2) [A002618].
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LINKS
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Table of n, a(n) for n=1..78.
Peter Luschny, Sequences related to Euler's totient function.
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EXAMPLE
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1
1,2
1,1,6
1,2,2,8
1,1,2,2,20
1,2,6,4,4,12
1,1,2,2,4,2,42
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MAPLE
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A181538 := (n, k) -> igcd(n, k)*phi(k);
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MATHEMATICA
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t[n_, k_] := Block[{j = Divisors@ k}, Plus @@ (#*MoebiusMu[k/#] & /@ j)] GCD[n, k]; Table[ t[n, k], {n, 12}, {k, n}] // Flatten (* From Robert G. Wilson v, Jan 19 2011 *)
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CROSSREFS
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Cf. Row sums of triangle A181540.
Sequence in context: A152656 A096162 A053383 * A125731 A123361 A179380
Adjacent sequences: A181535 A181536 A181537 * A181539 A181540 A181541
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KEYWORD
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nonn,tabl
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AUTHOR
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Peter Luschny, Oct 29 2010
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STATUS
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approved
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