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a(n) = 1 if A342001(n) is squarefree, and 0 otherwise.
3

%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