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%I A354874 #10 Jun 12 2022 15:38:51
%S A354874 0,0,1,1,0,1,1,1,0,1,1,1,0,1,0,0,0,1,1,1,0,1,1,1,0,1,1,0,0,1,1,1,0,1,
%T A354874 1,0,0,1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0,0,1,1,1,0,1,1,1,0,0,1,1,
%U A354874 0,1,1,1,0,1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0,1,0,0,0,1,1,0,0,1,1,1,0,1,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1
%N A354874 a(n) = 1 if A003415(n) is squarefree, otherwise 0.
%H A354874 Antti Karttunen, <a href="/A354874/b354874.txt">Table of n, a(n) for n = 0..100000</a>
%H A354874 <a href="/index/Ch#char_fns">Index entries for characteristic functions</a>
%F A354874 a(0) = a(1) = 0, for n > 1, a(n) = A008966(A003415(n)).
%F A354874 For n > 0, a(n) = A010051(n) + A341994(n), a(n) <= A212793(n).
%F A354874 For n > 1, a(n) = abs(A229343(n)).
%t A354874 d[0] = d[1] = 0; d[n_] := n * Plus @@ ((Last[#]/First[#]) & /@ FactorInteger[n]); a[n_] := If[SquareFreeQ[d[n]], 1, 0]; Array[a, 100, 0] (* _Amiram Eldar_, Jun 11 2022 *)
%o A354874 (PARI)
%o A354874 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A354874 A354874(n) = (issquarefree(A003415(n)));
%Y A354874 Characteristic function of A328393.
%Y A354874 Cf. A003415, A008966, A010051, A212793, A229343, A341994.
%K A354874 nonn
%O A354874 0
%A A354874 _Antti Karttunen_, Jun 11 2022

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