Conjecture: A111075(n) is odd whenever: (i) n = m^2 for all m>=1 such that 3 does not divide m, or (ii) n = 3*A028982(m) for all m>=1. Also, A028982 gives "Union of nonzero squares and twice squares."

It is not difficult to show that the conjecture is true. - Max Alekseyev, Oct 12 2005