%I #16 Dec 17 2024 13:01:45
%S 1,0,1,1,0,0,0,0,1,1,0,1,0,1,0,1,0,0,0,0,0,1,0,0,1,1,1,0,0,1,0,0,0,1,
%T 1,1,0,1,0,1,0,1,0,0,0,1,0,1,1,0,0,0,0,0,1,1,0,1,0,0,0,1,0,1,1,1,0,0,
%U 0,0,0,0,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0,1,0,1,0,1,1
%N a(n) = 1 if A373149(n) is even, otherwise 0, where A373149 is fully additive with a(2) = 1 and a(p) = prevprime(p) for odd primes p.
%H Antti Karttunen, <a href="/A373585/b373585.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(n) = A059841(A373149(n)).
%F a(n) = A059841(A001222(n) - A007949(n)).
%t Array[Boole[EvenQ[PrimeOmega[#] - IntegerExponent[#, 3]]] &, 100] (* _Paolo Xausa_, Dec 17 2024 *)
%o (PARI)
%o A373149(n) = { my(f = factor(n)); sum(i = 1, #f~, f[i, 2]*if(2==f[i, 1], 1, precprime(f[i, 1] - 1))); };
%o A373585(n) = !(A373149(n)%2);
%o (PARI) A373585(n) = !((bigomega(n)-valuation(n,3))%2);
%Y Characteristic function of A373586, whose complement A373587 gives the positions of 0's.
%Y Cf. A001222, A007949, A059841, A373149.
%K nonn
%O 1
%A _Antti Karttunen_, Jun 12 2024