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 A181552 T(n,k) = gcd(n,k) A181549(k), triangle read by rows. 2
 1, 1, 6, 1, 3, 12, 1, 6, 4, 20, 1, 3, 4, 5, 30, 1, 6, 12, 10, 6, 72, 1, 3, 4, 5, 6, 12, 56, 1, 6, 4, 20, 6, 24, 8, 80, 1, 3, 12, 5, 6, 36, 8, 10, 99, 1, 6, 4, 10, 30, 24, 8, 20, 11, 180, 1, 3, 4, 5, 6, 12, 8, 10, 11, 18, 132, 1, 6, 12, 20, 6, 72, 8, 40, 33, 36, 12, 240 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS A181549(n) = sum{k|n} k mu_2(n/k) is a variant of Euler's phi function relative to the Moebius function of order 2. LINKS Peter Luschny, Sequences related to Euler's totient function. EXAMPLE 1, 1,6, 1,3,12, 1,6,.4,20, 1,3,.4,.5,30, 1,6,12,10,.6,72, 1,3,.4,.5,.6,12,56, 1,6,.4,20,.6,24,.8,80, MAPLE A181552 := (n, k) -> igcd(n, k)*A181549(k); MATHEMATICA mu2[1] = 1; mu2[n_] := Sum[Boole[Divisible[n, d^2]]*MoebiusMu[n/d^2]*MoebiusMu[n/d], {d, Divisors[n]}]; A181549[n_] := Sum[k*mu2[n/k], {k, Divisors[n]}]; t[n_, k_] := GCD[n, k]*A181549[k]; Table[t[n, k], {n, 1, 12}, {k, 1, n}] // Flatten (* Jean-François Alcover, Feb 05 2014 *) CROSSREFS Cf. A130212, A181538, row sums of triangle is A181553. Sequence in context: A259731 A176399 A273081 * A294347 A229606 A101023 Adjacent sequences:  A181549 A181550 A181551 * A181553 A181554 A181555 KEYWORD nonn,tabl AUTHOR Peter Luschny, Oct 30 2010 STATUS approved

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Last modified September 25 09:32 EDT 2021. Contains 347654 sequences. (Running on oeis4.)