A354353 - OEIS

%I #17 Sep 19 2022 13:42:08

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

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

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

%N a(n) = 1 if n is either a squarefree composite or a power of squarefree composite, otherwise 0.

%H Antti Karttunen, <a href="/A354353/b354353.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 For all n >= 1, a(n) = a(A046523(n)).

%F For all n > 1, a(n) >= A354819(n).

%t a[1] = 0; a[n_] := If[Length[e = FactorInteger[n][[;; , 2]]] > 1 && SameQ @@ e, 1, 0]; Array[a, 105] (* _Amiram Eldar_, Jun 11 2022 *)

%o (PARI)

%o A354819(n) = ((1!=bigomega(n))&&issquarefree(n));

%o A354353(n) = ((n>1) && (A354819(n) || (ispower(n, , &k) && A354819(k))));

%Y Characteristic function of A182853.

%Y Cf. A001221, A008966, A046523, A227291, A354819.

%K nonn

%O 1

%A _Antti Karttunen_, Jun 10 2022