A181550 - OEIS

%I #13 Feb 05 2014 06:43:56

%S 1,2,3,3,3,4,4,6,4,5,5,6,4,5,6,6,9,8,5,6,12,7,9,8,5,6,12,8,8,12,8,10,

%T 6,12,8,10,9,12,12,10,6,12,8,10,11,10,15,12,10,12,12,8,10,11,18,11,15,

%U 12,10,12,12,8,10,11,18,12,12,18,16,15,12,24,8,10,11,18,12,20

%N T(n,k) = floor(n/k)*A181549(k), triangle read by rows.

%C A181549(n) = sum{k|n} k mu_2(n/k), 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 2, 3

%e 3, 3, 4

%e 4, 6, 4, 5

%e 5, 6, 4, 5, 6

%e 6, 9, 8, 5, 6, 12

%e 7, 9, 8, 5, 6, 12, 8

%e 8, 12, 8, 10, 6, 12, 8, 10

%p A181550 := (n,k) -> iquo(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_] := Floor[n/k]*A181549[k]; Table[t[n, k], {n, 1, 12}, {k, 1, n}] // Flatten (* _Jean-François Alcover_, Feb 05 2014 *)

%Y Cf. A130212, A181549.

%K nonn,tabl

%O 1,2

%A _Peter Luschny_, Oct 30 2010