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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
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
KEYWORD
nonn,tabl
AUTHOR
Peter Luschny, Oct 30 2010
STATUS
approved