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%I #7 Feb 05 2014 06:43:46
%S 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,
%T 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,
%U 4,5,6,12,8,10,11,18,132,1,6,12,20,6,72,8,40,33,36,12,240
%N T(n,k) = gcd(n,k) A181549(k), triangle read by rows.
%C 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.
%H Peter Luschny, Sequences related to <a href="http://www.oeis.org/wiki/User:Peter_Luschny/EulerTotient">Euler's totient</a> function.
%e 1,
%e 1,6,
%e 1,3,12,
%e 1,6,.4,20,
%e 1,3,.4,.5,30,
%e 1,6,12,10,.6,72,
%e 1,3,.4,.5,.6,12,56,
%e 1,6,.4,20,.6,24,.8,80,
%p A181552 := (n,k) -> igcd(n,k)*A181549(k);
%t 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 *)
%Y Cf. A130212, A181538, row sums of triangle is A181553.
%K nonn,tabl
%O 1,3
%A _Peter Luschny_, Oct 30 2010
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