A short note on the divisibility of class numbers of real quadratic fields

For any integer l >= 1, let p(1), p(2),..., p(l+2) be distinct prime numbers >= 5. For all real numbers X > 1, we let N-3,N-l (X) denote the number of real quadratic fields K whose absolute discriminant d(K) <= X and d(K) is divisible by (p(1)... p(l+2)) together with the class number h(K) of K divisible by 2(l).3. Then, in this short note, by following the method in [3], we prove that N-3,N-l (X) >> X-7/8 for all large enough X's.