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A325144 a(n) = - Sum_{d | n} (-1)^d *a(d) if n != 1, a(1) = 1.

%I A325144 #9 Apr 19 2019 12:14:15
%S A325144 0,1,1,1,0,1,1,1,0,2,1,1,0,1,1,3,0,1,2,1,0,3,1,1,0,2,1,4,0,1,3,1,0,3,
%T A325144 1,3,0,1,1,3,0,1,3,1,0,8,1,1,0,2,2,3,0,1,4,3,0,3,1,1,0,1,1,8,0,3,3,1,
%U A325144 0,3,3,1,0,1,1,8,0,3,3,1,0,8,1,1,0,3,1
%N A325144 a(n) = - Sum_{d | n} (-1)^d *a(d) if n != 1, a(1) = 1.
%H A325144 Peter Luschny, <a href="/A325144/b325144.txt">Table of n, a(n) for n = 0..10000</a>
%F A325144 a(4*n) = 0 for n >= 0.
%F A325144 a(2*n) = 0 for n <= 0.
%F A325144 if n is prime then a(n) = 1.
%F A325144 if n is squarefree then a(n) is odd (A005117).
%F A325144 if a(n) is even then n is not squarefree (A013929) (for n > 0).
%p A325144 a := proc(n) option remember; `if`(n = 1, 1,
%p A325144 -add((-1)^d*a(d), d = numtheory:-divisors(n) minus {n})) end:
%p A325144 seq(a(n), n = 0..86);
%Y A325144 Cf. A008683, A005117, A013929.
%K A325144 nonn
%O A325144 0,10
%A A325144 _Peter Luschny_, Apr 19 2019