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