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%I #13 Aug 11 2018 21:59:27
%S 1,0,0,-1,0,0,0,0,-1,0,0,1,0,0,0,0,0,1,0,1,0,0,0,0,-1,0,0,1,0,0,0,0,0,
%T 0,0,-1,0,0,0,0,0,0,0,1,1,0,0,0,-1,1,0,1,0,0,0,0,0,0,0,-1,0,0,1,0,0,0,
%U 0,1,0,0,0,1,0,0,1,1,0,0,0,0,0,0,0,-1,0,0,0,0,0,-1,0,1,0,0,0,0,0,1,1,-1,0,0,0,0,0
%N a(n) = Sum_{d|n, d = 1 or not a perfect power} mu(n/d).
%C The Moebius function mu is defined by mu(n) = (-1)^k if n is a product of k distinct primes and mu(n) = 0 otherwise.
%C Up to n = 10^7 this sequence only takes values in {-2, -1, 0, 1, 2}. Is this true in general?
%H Antti Karttunen, <a href="/A304362/b304362.txt">Table of n, a(n) for n = 1..65537</a>
%F a(n) = mu(n) + Sum_{d * e = n, d in A007916, e in A005117} (-1)^omega(e), where mu = A008683 and omega = A001221.
%t Table[Sum[If[GCD@@FactorInteger[d][[All,2]]===1,MoebiusMu[n/d],0],{d,Divisors[n]}],{n,100}]
%o (PARI) A304362(n) = sumdiv(n,d,if(!ispower(d),moebius(n/d),0)); \\ _Antti Karttunen_, Jul 29 2018
%Y Cf. A000005, A000961, A001221, A001597, A001694, A005117, A007916, A008683, A091050, A203025, A304326, A304327, A304364, A304365, A304369.
%K sign
%O 1
%A _Gus Wiseman_, May 11 2018
%E More terms from _Antti Karttunen_, Jul 29 2018
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