A181552 - OEIS

%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