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 A181538 T(n, k) = sum_(1 <= j <= k) [j | k] j mu(k / j) gcd(n, k), triangle read by rows. 3
 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 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS T(n,k) = gcd(n,k) phi(k). Can be seen as a generalization of n -> phi(n^2) [A002618]. LINKS Peter Luschny, Sequences related to Euler's totient function. EXAMPLE 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 MAPLE A181538 := (n, k) -> igcd(n, k)*phi(k); MATHEMATICA 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 *) CROSSREFS Cf. Row sums of triangle A181540. Sequence in context: A152656 A096162 A053383 * A125731 A123361 A179380 Adjacent sequences:  A181535 A181536 A181537 * A181539 A181540 A181541 KEYWORD nonn,tabl AUTHOR Peter Luschny, Oct 29 2010 STATUS approved

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