A353669 - OEIS

%I #11 Sep 19 2022 15:31:17

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

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

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

%N a(n) = 1 if n is a nonsquare that has an even number of prime factors with multiplicity, otherwise 0.

%H Antti Karttunen, <a href="/A353669/b353669.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) = if A001222(n) and A000005(n) are both even, otherwise 0.

%F a(n) = A065043(n) - A010052(n).

%t Table[If[!IntegerQ[Sqrt[n]]&&EvenQ[PrimeOmega[n]],1,0],{n,150}] (* _Harvey P. Dale_, Sep 19 2022 *)

%o (PARI) A353669(n) = (!issquare(n) && !(bigomega(n)%2));

%o (PARI) A353669(n) = (0==((bitxor(bigomega(n),numdiv(n)))%2));

%Y Characteristic function of A119899.

%Y Cf. A000005, A001222, A010052, A065043.

%K nonn

%O 1

%A _Antti Karttunen_, May 04 2022