%I #13 Jan 14 2024 20:35:18
%S 0,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,1,1,1,0,1,1,1,1,1,1,1,0,1,1,1,1,1,1,
%T 0,1,1,1,0,1,1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,1,1,1,1,1,1,1,1,0,1,1,0,
%U 1,1,1,1,1,1,1,0,0,1,1,1,0,1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,1,1,1,1,1,1,1,1,0,1,1,0,1,1,1,0,0,1,1,0,1,1
%N a(n) = 1 if A342001(n) is squarefree, and 0 otherwise.
%C Question: What is the asymptotic mean of this and related sequences like A354874 and A368914?
%H Antti Karttunen, <a href="/A368912/b368912.txt">Table of n, a(n) for n = 1..100000</a>
%H <a href="/index/Ch#char_fns">Index entries for characteristic functions</a>
%F a(1) = 0, and for n > 1, a(n) = A008966(A342001(n)).
%F For all n >= 1, A354874(n) <= a(n) <= A368914(n).
%o (PARI)
%o A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A003557(n) = (n/factorback(factorint(n)[, 1]));
%o A342001(n) = (A003415(n) / A003557(n));
%o A368912(n) = ((n>1)&&issquarefree(A342001(n)));
%Y Characteristic function of A368902.
%Y Cf. A003415, A008966, A342001, A354874, A368914.
%K nonn
%O 1
%A _Antti Karttunen_, Jan 10 2024