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a(n) = 1 if all the exponents in the prime factorization of n are distinct, and 0 otherwise.
7

%I #15 Jul 30 2022 08:18:47

%S 1,1,1,1,1,0,1,1,1,0,1,1,1,0,0,1,1,1,1,1,0,0,1,1,1,0,1,1,1,0,1,1,0,0,

%T 0,0,1,0,0,1,1,0,1,1,1,0,1,1,1,1,0,1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,1,

%U 0,0,1,1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0,0,0,1,1,1,1,0,1,0,1,1,0

%N a(n) = 1 if all the exponents in the prime factorization of n are distinct, and 0 otherwise.

%H Antti Karttunen, <a href="/A351564/b351564.txt">Table of n, a(n) for n = 1..65537</a>

%H <a href="/index/Ch#char_fns">Index entries for characteristic functions</a>.

%H <a href="/index/Eu#epf">Index entries for sequences computed from exponents in factorization of n</a>.

%F a(n) = A008966(A181819(n)).

%e For n = 4 = 2^2, all the exponents present [2] are distinct, therefore a(4) = 1.

%e For n = 300 = 2^2 * 3^1 * 5^2, the exponents are [2, 1, 2], thus they are not all distinct, therefore a(300) = 0.

%t a[n_] := If[UnsameQ @@ FactorInteger[n][[;;, 2]], 1, 0]; Array[a, 100] (* _Amiram Eldar_, Jul 30 2022 *)

%o (PARI) A351564(n) = issquarefree(factorback(apply(e->prime(e),(factor(n)[,2]))));

%Y Characteristic function of A130091.

%Y Cf. A008966, A181819, A327498, A327499.

%K nonn

%O 1

%A _Antti Karttunen_, Apr 02 2022