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%I #14 Jan 05 2023 03:20:32
%S 0,0,0,1,0,0,0,0,1,0,0,1,0,0,0,0,0,1,0,1,0,0,0,0,1,0,0,1,0,0,0,0,0,0,
%T 0,1,0,0,0,0,0,0,0,1,1,0,0,0,1,1,0,1,0,0,0,0,0,0,0,1,0,0,1,0,0,0,0,1,
%U 0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,1,0,0,0,0,0,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,1
%N a(n) = 1 if n is cubefree, but not squarefree, otherwise 0.
%H Antti Karttunen, <a href="/A359429/b359429.txt">Table of n, a(n) for n = 1..100000</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) = A107078(n) * A212793(n) = A212793(n) - A008966(n).
%F a(n) = [A072411(n) == 2] = [A290107(n) == 2], where [ ] is the Iverson bracket.
%F a(n) >= A359474(n).
%F Sum_{k=1..n} a(k) ~ c * n, where c = 1/zeta(3) - 1/zeta(2) = A088453 - A059956 = 0.22398... . - _Amiram Eldar_, Jan 05 2023
%t a[n_] := If[Max[FactorInteger[n][[;; , 2]]] == 2, 1, 0]; Array[a, 100] (* _Amiram Eldar_, Jan 05 2023 *)
%o (PARI)
%o A212793(n) = {f = factor(n); for (i=1, #f~, if ((f[i, 2]) >=3, return(0)); ); return (1); }; \\ From A212793.
%o A359429(n) = (A212793(n)-issquarefree(n));
%Y Characteristic function of A067259.
%Y Cf. A008966, A072411, A107078, A212793, A290107, A359474.
%Y Cf. A059956, A088453.
%K nonn
%O 1
%A _Antti Karttunen_, Jan 04 2023
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